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The minimal power iteration of a number $n$ is defined as follows:

$$textMPI(n):=n^textmin(textdigits(n))$$

That is, $n$ raised to the lowest digit in $n$. For example, $textMPI(32)=32^2=1024$ and $textMPI(1234)=1234^1=1234$.

The minimal power root of a number $n$ is defined as the number obtained from repeatedly applying $textMPI$ until a fixed point is found. Here is a table of the minimal power roots of numbers between 1 and 25:

 n MPR(n)
--------------------------
 1 1
 2 1
 3 531441
 4 1
 5 3125
 6 4738381338321616896
 7 1
 8 16777216
 9 1
 10 1
 11 11
 12 12
 13 13
 14 14
 15 15
 16 16
 17 17
 18 18
 19 19
 20 1
 21 21
 22 1
 23 279841
 24 1
 25 1

Challenge: Generate the numbers whose minimal power root is not equal to 1 or itself.

Here are the first 50 numbers in this sequence:

3, 5, 6, 8, 23, 26, 27, 29, 35, 36, 39, 42, 47, 53, 59, 64, 72, 76, 78, 82, 83, 84, 92, 222, 223, 227, 228, 229, 233, 237, 239, 254, 263, 267, 268, 269, 273, 276, 277, 278, 279, 285, 286, 287, 289, 296, 335, 338, 339, 342

Rules

You may generate the first n numbers of this sequence (0- or 1-indexed), generate the nth term, create a generator which calculates these terms, output infinitely many of them, etc.

You may take input and give output in any base, but the calculations for MPR must be in base 10. E.g., you may take input ### (in unary) and output ### ##### ###### (in unary)

You must yield numbers. You may not (e.g.) output "3", "5", "6", since those are strings. 3, 5, 6 and 3 5 6 are both valid, however. Outputting 2 3, "23", or twenty-three are all considered invalid representations of the number 23. (Again, you may use any base to represent these numbers.)

This is a code-golf, so the shortest code (in bytes) wins.

edited 45 mins ago

asked 58 mins ago

Conor O'Brien

28.5k263158

add a commentÂ |Â

up vote
4
down vote

favorite

The minimal power iteration of a number $n$ is defined as follows:

$$textMPI(n):=n^textmin(textdigits(n))$$

That is, $n$ raised to the lowest digit in $n$. For example, $textMPI(32)=32^2=1024$ and $textMPI(1234)=1234^1=1234$.

 n MPR(n)
--------------------------
 1 1
 2 1
 3 531441
 4 1
 5 3125
 6 4738381338321616896
 7 1
 8 16777216
 9 1
 10 1
 11 11
 12 12
 13 13
 14 14
 15 15
 16 16
 17 17
 18 18
 19 19
 20 1
 21 21
 22 1
 23 279841
 24 1
 25 1

Challenge: Generate the numbers whose minimal power root is not equal to 1 or itself.

Here are the first 50 numbers in this sequence:

3, 5, 6, 8, 23, 26, 27, 29, 35, 36, 39, 42, 47, 53, 59, 64, 72, 76, 78, 82, 83, 84, 92, 222, 223, 227, 228, 229, 233, 237, 239, 254, 263, 267, 268, 269, 273, 276, 277, 278, 279, 285, 286, 287, 289, 296, 335, 338, 339, 342

Rules

You may generate the first n numbers of this sequence (0- or 1-indexed), generate the nth term, create a generator which calculates these terms, output infinitely many of them, etc.

You may take input and give output in any base, but the calculations for MPR must be in base 10. E.g., you may take input ### (in unary) and output ### ##### ###### (in unary)

You must yield numbers. You may not (e.g.) output "3", "5", "6", since those are strings. 3, 5, 6 and 3 5 6 are both valid, however. Outputting 2 3, "23", or twenty-three are all considered invalid representations of the number 23. (Again, you may use any base to represent these numbers.)

This is a code-golf, so the shortest code (in bytes) wins.

edited 45 mins ago

asked 58 mins ago

Conor O'Brien

28.5k263158

add a commentÂ |Â

up vote
4
down vote

favorite

The minimal power iteration of a number $n$ is defined as follows:

$$textMPI(n):=n^textmin(textdigits(n))$$

That is, $n$ raised to the lowest digit in $n$. For example, $textMPI(32)=32^2=1024$ and $textMPI(1234)=1234^1=1234$.

 n MPR(n)
--------------------------
 1 1
 2 1
 3 531441
 4 1
 5 3125
 6 4738381338321616896
 7 1
 8 16777216
 9 1
 10 1
 11 11
 12 12
 13 13
 14 14
 15 15
 16 16
 17 17
 18 18
 19 19
 20 1
 21 21
 22 1
 23 279841
 24 1
 25 1

Challenge: Generate the numbers whose minimal power root is not equal to 1 or itself.

Here are the first 50 numbers in this sequence:

3, 5, 6, 8, 23, 26, 27, 29, 35, 36, 39, 42, 47, 53, 59, 64, 72, 76, 78, 82, 83, 84, 92, 222, 223, 227, 228, 229, 233, 237, 239, 254, 263, 267, 268, 269, 273, 276, 277, 278, 279, 285, 286, 287, 289, 296, 335, 338, 339, 342

Rules

You may generate the first n numbers of this sequence (0- or 1-indexed), generate the nth term, create a generator which calculates these terms, output infinitely many of them, etc.

You may take input and give output in any base, but the calculations for MPR must be in base 10. E.g., you may take input ### (in unary) and output ### ##### ###### (in unary)

You must yield numbers. You may not (e.g.) output "3", "5", "6", since those are strings. 3, 5, 6 and 3 5 6 are both valid, however. Outputting 2 3, "23", or twenty-three are all considered invalid representations of the number 23. (Again, you may use any base to represent these numbers.)

This is a code-golf, so the shortest code (in bytes) wins.

edited 45 mins ago

asked 58 mins ago

Conor O'Brien

28.5k263158

The minimal power iteration of a number $n$ is defined as follows:

$$textMPI(n):=n^textmin(textdigits(n))$$

That is, $n$ raised to the lowest digit in $n$. For example, $textMPI(32)=32^2=1024$ and $textMPI(1234)=1234^1=1234$.

 n MPR(n)
--------------------------
 1 1
 2 1
 3 531441
 4 1
 5 3125
 6 4738381338321616896
 7 1
 8 16777216
 9 1
 10 1
 11 11
 12 12
 13 13
 14 14
 15 15
 16 16
 17 17
 18 18
 19 19
 20 1
 21 21
 22 1
 23 279841
 24 1
 25 1

Challenge: Generate the numbers whose minimal power root is not equal to 1 or itself.

Here are the first 50 numbers in this sequence:

3, 5, 6, 8, 23, 26, 27, 29, 35, 36, 39, 42, 47, 53, 59, 64, 72, 76, 78, 82, 83, 84, 92, 222, 223, 227, 228, 229, 233, 237, 239, 254, 263, 267, 268, 269, 273, 276, 277, 278, 279, 285, 286, 287, 289, 296, 335, 338, 339, 342

Rules

You may generate the first n numbers of this sequence (0- or 1-indexed), generate the nth term, create a generator which calculates these terms, output infinitely many of them, etc.

You may take input and give output in any base, but the calculations for MPR must be in base 10. E.g., you may take input ### (in unary) and output ### ##### ###### (in unary)

You must yield numbers. You may not (e.g.) output "3", "5", "6", since those are strings. 3, 5, 6 and 3 5 6 are both valid, however. Outputting 2 3, "23", or twenty-three are all considered invalid representations of the number 23. (Again, you may use any base to represent these numbers.)

This is a code-golf, so the shortest code (in bytes) wins.

code-golf number sequence

edited 45 mins ago

asked 58 mins ago

Conor O'Brien

28.5k263158

edited 45 mins ago

asked 58 mins ago

Conor O'Brien

28.5k263158

edited 45 mins ago

asked 58 mins ago

Conor O'Brien

28.5k263158

asked 58 mins ago

Conor O'Brien

28.5k263158

asked 58 mins ago

Conor O'Brien

28.5k263158

add a commentÂ |Â

5 Answers
5

active

oldest

votes

up vote
0
down vote

Jelly, 14 bytes

3*DÃ¡Â¹Â‚$$ÃƒÂLÃ¡Â¸ÂŸ1,$Ã†ÂŠ#

Try it online!

answered 43 mins ago

Erik the Outgolfer

29.8k42899

add a commentÂ |Â

up vote
0
down vote

Mathematica, 59 bytes

Select[Range@#,1<FixedPoint[#^Min@IntegerDigits@#&,#]!=#&]&

Pure function. Takes a number as input, and returns the list of terms up to that number as output. Nothing very complicated here.

answered 35 mins ago

LegionMammal978

14.8k41752

add a commentÂ |Â

up vote
0
down vote

Pyth, 10 bytes

.f>u^GshS`

Try it online!

This generates a list of the first $ n $ such numbers. The auto-filled program has GZZQ as a suffix. This simply finds (.f) the first Q numbers that have a minimal power root u^GshS`G greater than itself Z.

The minimal power root code works by finding a fixed point u of raising the current number G to the power of it's minimal digit, which is the same as the first digit (h) sorted lexicographically (S), then converted back to an integer (s).

answered 28 mins ago

FryAmTheEggman

14.6k32481

add a commentÂ |Â

up vote
0
down vote

Perl 6, 24 bytes

$_,$_**.comb.min...*

Try it online!

Returns an infinite sequence.

answered 22 mins ago

nwellnhof

4,388817

add a commentÂ |Â

up vote
0
down vote

Jelly, 10 bytes

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ#

Try it online!

How?

Counts up starting a n=1 until input truthy results of a monadic function are encountered and yields those ns.

The function repeatedly applies another monadic function starting with x=n and collects the values of x until the results are no longer unique. (e.g.: 19 yields [19]; 23 yields [23,529,279841]; 24 yields [24, 576, 63403380965376, 1]; etc...) and then dequeues the result (removes the leftmost value), complements all the values (1-x) and uses ÃˆÂ¦ to yield 0 when there is a zero in the list or if it's empty.

The innermost function raises the current x to all the digits of x and then keeps the minimum (doing this is a byte save over finding the minimum digit first).

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ# - Main Link (call the input number I)
 # - count up from 1 and yield the first I for which this yields a truthy value:
 Ã‚Âµ - a monadic chain:
 Ã†Â¬ - collect until results are not unique:
 Ã†ÂŠ - last three links as a monad:
 D - convert to a list of decimal digits
* - exponentiate
 Ã¡Â¹Â‚ - minimum
 Ã¡Â¸ÂŠ - dequeue
 C - compliment
 ÃˆÂ¦ - any-and-all?

edited 6 mins ago

answered 33 mins ago

Jonathan Allan

49k534161

add a commentÂ |Â

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5 Answers
5

active

oldest

votes

5 Answers
5

active

oldest

votes

up vote
0
down vote

Jelly, 14 bytes

3*DÃ¡Â¹Â‚$$ÃƒÂLÃ¡Â¸ÂŸ1,$Ã†ÂŠ#

Try it online!

answered 43 mins ago

Erik the Outgolfer

29.8k42899

add a commentÂ |Â

up vote
0
down vote

Jelly, 14 bytes

3*DÃ¡Â¹Â‚$$ÃƒÂLÃ¡Â¸ÂŸ1,$Ã†ÂŠ#

Try it online!

answered 43 mins ago

Erik the Outgolfer

29.8k42899

add a commentÂ |Â

up vote
0
down vote

Jelly, 14 bytes

3*DÃ¡Â¹Â‚$$ÃƒÂLÃ¡Â¸ÂŸ1,$Ã†ÂŠ#

Try it online!

answered 43 mins ago

Erik the Outgolfer

29.8k42899

Jelly, 14 bytes

3*DÃ¡Â¹Â‚$$ÃƒÂLÃ¡Â¸ÂŸ1,$Ã†ÂŠ#

Try it online!

answered 43 mins ago

Erik the Outgolfer

29.8k42899

answered 43 mins ago

Erik the Outgolfer

29.8k42899

answered 43 mins ago

Erik the Outgolfer

29.8k42899

answered 43 mins ago

Erik the Outgolfer

29.8k42899

add a commentÂ |Â

up vote
0
down vote

Mathematica, 59 bytes

Select[Range@#,1<FixedPoint[#^Min@IntegerDigits@#&,#]!=#&]&

Pure function. Takes a number as input, and returns the list of terms up to that number as output. Nothing very complicated here.

answered 35 mins ago

LegionMammal978

14.8k41752

add a commentÂ |Â

up vote
0
down vote

Mathematica, 59 bytes

Select[Range@#,1<FixedPoint[#^Min@IntegerDigits@#&,#]!=#&]&

Pure function. Takes a number as input, and returns the list of terms up to that number as output. Nothing very complicated here.

answered 35 mins ago

LegionMammal978

14.8k41752

add a commentÂ |Â

up vote
0
down vote

Mathematica, 59 bytes

Select[Range@#,1<FixedPoint[#^Min@IntegerDigits@#&,#]!=#&]&

Pure function. Takes a number as input, and returns the list of terms up to that number as output. Nothing very complicated here.

answered 35 mins ago

LegionMammal978

14.8k41752

Mathematica, 59 bytes

Select[Range@#,1<FixedPoint[#^Min@IntegerDigits@#&,#]!=#&]&

Pure function. Takes a number as input, and returns the list of terms up to that number as output. Nothing very complicated here.

answered 35 mins ago

LegionMammal978

14.8k41752

answered 35 mins ago

LegionMammal978

14.8k41752

answered 35 mins ago

LegionMammal978

14.8k41752

answered 35 mins ago

LegionMammal978

14.8k41752

add a commentÂ |Â

up vote
0
down vote

Pyth, 10 bytes

.f>u^GshS`

Try it online!

answered 28 mins ago

FryAmTheEggman

14.6k32481

add a commentÂ |Â

up vote
0
down vote

Pyth, 10 bytes

.f>u^GshS`

Try it online!

answered 28 mins ago

FryAmTheEggman

14.6k32481

add a commentÂ |Â

up vote
0
down vote

Pyth, 10 bytes

.f>u^GshS`

Try it online!

answered 28 mins ago

FryAmTheEggman

14.6k32481

Pyth, 10 bytes

.f>u^GshS`

Try it online!

answered 28 mins ago

FryAmTheEggman

14.6k32481

answered 28 mins ago

FryAmTheEggman

14.6k32481

answered 28 mins ago

FryAmTheEggman

14.6k32481

answered 28 mins ago

FryAmTheEggman

14.6k32481

add a commentÂ |Â

up vote
0
down vote

Perl 6, 24 bytes

$_,$_**.comb.min...*

Try it online!

Returns an infinite sequence.

answered 22 mins ago

nwellnhof

4,388817

add a commentÂ |Â

up vote
0
down vote

Perl 6, 24 bytes

$_,$_**.comb.min...*

Try it online!

Returns an infinite sequence.

answered 22 mins ago

nwellnhof

4,388817

add a commentÂ |Â

up vote
0
down vote

Perl 6, 24 bytes

$_,$_**.comb.min...*

Try it online!

Returns an infinite sequence.

answered 22 mins ago

nwellnhof

4,388817

Perl 6, 24 bytes

$_,$_**.comb.min...*

Try it online!

Returns an infinite sequence.

answered 22 mins ago

nwellnhof

4,388817

answered 22 mins ago

nwellnhof

4,388817

answered 22 mins ago

nwellnhof

4,388817

answered 22 mins ago

nwellnhof

4,388817

add a commentÂ |Â

up vote
0
down vote

Jelly, 10 bytes

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ#

Try it online!

How?

Counts up starting a n=1 until input truthy results of a monadic function are encountered and yields those ns.

The innermost function raises the current x to all the digits of x and then keeps the minimum (doing this is a byte save over finding the minimum digit first).

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ# - Main Link (call the input number I)
 # - count up from 1 and yield the first I for which this yields a truthy value:
 Ã‚Âµ - a monadic chain:
 Ã†Â¬ - collect until results are not unique:
 Ã†ÂŠ - last three links as a monad:
 D - convert to a list of decimal digits
* - exponentiate
 Ã¡Â¹Â‚ - minimum
 Ã¡Â¸ÂŠ - dequeue
 C - compliment
 ÃˆÂ¦ - any-and-all?

edited 6 mins ago

answered 33 mins ago

Jonathan Allan

49k534161

add a commentÂ |Â

up vote
0
down vote

Jelly, 10 bytes

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ#

Try it online!

How?

Counts up starting a n=1 until input truthy results of a monadic function are encountered and yields those ns.

The innermost function raises the current x to all the digits of x and then keeps the minimum (doing this is a byte save over finding the minimum digit first).

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ# - Main Link (call the input number I)
 # - count up from 1 and yield the first I for which this yields a truthy value:
 Ã‚Âµ - a monadic chain:
 Ã†Â¬ - collect until results are not unique:
 Ã†ÂŠ - last three links as a monad:
 D - convert to a list of decimal digits
* - exponentiate
 Ã¡Â¹Â‚ - minimum
 Ã¡Â¸ÂŠ - dequeue
 C - compliment
 ÃˆÂ¦ - any-and-all?

edited 6 mins ago

answered 33 mins ago

Jonathan Allan

49k534161

add a commentÂ |Â

up vote
0
down vote

Jelly, 10 bytes

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ#

Try it online!

How?

Counts up starting a n=1 until input truthy results of a monadic function are encountered and yields those ns.

The innermost function raises the current x to all the digits of x and then keeps the minimum (doing this is a byte save over finding the minimum digit first).

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ# - Main Link (call the input number I)
 # - count up from 1 and yield the first I for which this yields a truthy value:
 Ã‚Âµ - a monadic chain:
 Ã†Â¬ - collect until results are not unique:
 Ã†ÂŠ - last three links as a monad:
 D - convert to a list of decimal digits
* - exponentiate
 Ã¡Â¹Â‚ - minimum
 Ã¡Â¸ÂŠ - dequeue
 C - compliment
 ÃˆÂ¦ - any-and-all?

edited 6 mins ago

answered 33 mins ago

Jonathan Allan

49k534161

Jelly, 10 bytes

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ#

Try it online!

How?

Counts up starting a n=1 until input truthy results of a monadic function are encountered and yields those ns.

The innermost function raises the current x to all the digits of x and then keeps the minimum (doing this is a byte save over finding the minimum digit first).

*DÃ¡Â¹Â‚Ã†ÂŠÃ†Â¬Ã¡Â¸ÂŠCÃˆÂ¦Ã‚Âµ# - Main Link (call the input number I)
 # - count up from 1 and yield the first I for which this yields a truthy value:
 Ã‚Âµ - a monadic chain:
 Ã†Â¬ - collect until results are not unique:
 Ã†ÂŠ - last three links as a monad:
 D - convert to a list of decimal digits
* - exponentiate
 Ã¡Â¹Â‚ - minimum
 Ã¡Â¸ÂŠ - dequeue
 C - compliment
 ÃˆÂ¦ - any-and-all?

edited 6 mins ago

answered 33 mins ago

Jonathan Allan

49k534161

edited 6 mins ago

answered 33 mins ago

Jonathan Allan

49k534161

answered 33 mins ago

Jonathan Allan

49k534161

answered 33 mins ago

Jonathan Allan

49k534161

add a commentÂ |Â

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Minimal Power Root

Rules

Rules

Rules

Rules

5 Answers 5

Jelly, 14 bytes

Mathematica, 59 bytes

Pyth, 10 bytes

Perl 6, 24 bytes

Jelly, 10 bytes

How?

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5 Answers 5

5 Answers 5

Jelly, 14 bytes

Jelly, 14 bytes

Jelly, 14 bytes

Jelly, 14 bytes

Mathematica, 59 bytes

Mathematica, 59 bytes

Mathematica, 59 bytes

Mathematica, 59 bytes

Pyth, 10 bytes

Pyth, 10 bytes

Pyth, 10 bytes

Pyth, 10 bytes

Perl 6, 24 bytes

Perl 6, 24 bytes

Perl 6, 24 bytes

Perl 6, 24 bytes

Jelly, 10 bytes

How?

Jelly, 10 bytes

How?

Jelly, 10 bytes

How?

Jelly, 10 bytes

How?

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