Doubled digit numbers

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Some cute results have every digit doubled.



beginalign
99225500774400 = & frac40!31! \[8pt]
33554433 = & 2^25 +1 \[8pt]
222277 = & -22^2^2+77^3 \[8pt]
8811551199 = & 95^5 + 64^5 \[8pt]
7755660000 = & 95^5 + 65^4 \[8pt]
334444448888 = & 6942^3 - 10^8 \[8pt]
11881133 = & 26^5 - 3^5 \[8pt]
0.0011223344556677ldots = & frac 1 891 \[8pt]
22116600446655008888446677444 = & 148716510336462^2 \[8pt]
endalign



The last is from A079036. What are other cute examples?






soft-question recreational-mathematics







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  • 4




    $1/891$ isn't quite all that: $0.overline001122334455667789$. (But cute nonetheless!)
    – John
    3 hours ago















up vote
7
down vote

favorite
1












Some cute results have every digit doubled.



beginalign
99225500774400 = & frac40!31! \[8pt]
33554433 = & 2^25 +1 \[8pt]
222277 = & -22^2^2+77^3 \[8pt]
8811551199 = & 95^5 + 64^5 \[8pt]
7755660000 = & 95^5 + 65^4 \[8pt]
334444448888 = & 6942^3 - 10^8 \[8pt]
11881133 = & 26^5 - 3^5 \[8pt]
0.0011223344556677ldots = & frac 1 891 \[8pt]
22116600446655008888446677444 = & 148716510336462^2 \[8pt]
endalign



The last is from A079036. What are other cute examples?






soft-question recreational-mathematics







share|cite|improve this question



















  • 4




    $1/891$ isn't quite all that: $0.overline001122334455667789$. (But cute nonetheless!)
    – John
    3 hours ago













up vote
7
down vote

favorite
1









up vote
7
down vote

favorite
1






1





Some cute results have every digit doubled.



beginalign
99225500774400 = & frac40!31! \[8pt]
33554433 = & 2^25 +1 \[8pt]
222277 = & -22^2^2+77^3 \[8pt]
8811551199 = & 95^5 + 64^5 \[8pt]
7755660000 = & 95^5 + 65^4 \[8pt]
334444448888 = & 6942^3 - 10^8 \[8pt]
11881133 = & 26^5 - 3^5 \[8pt]
0.0011223344556677ldots = & frac 1 891 \[8pt]
22116600446655008888446677444 = & 148716510336462^2 \[8pt]
endalign



The last is from A079036. What are other cute examples?






soft-question recreational-mathematics







share|cite|improve this question















Some cute results have every digit doubled.



beginalign
99225500774400 = & frac40!31! \[8pt]
33554433 = & 2^25 +1 \[8pt]
222277 = & -22^2^2+77^3 \[8pt]
8811551199 = & 95^5 + 64^5 \[8pt]
7755660000 = & 95^5 + 65^4 \[8pt]
334444448888 = & 6942^3 - 10^8 \[8pt]
11881133 = & 26^5 - 3^5 \[8pt]
0.0011223344556677ldots = & frac 1 891 \[8pt]
22116600446655008888446677444 = & 148716510336462^2 \[8pt]
endalign



The last is from A079036. What are other cute examples?






soft-question recreational-mathematics




soft-question recreational-mathematics






share|cite|improve this question















share|cite|improve this question













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share|cite|improve this question








edited 24 mins ago

























asked 3 hours ago









Ed Pegg

9,41332588




9,41332588







  • 4




    $1/891$ isn't quite all that: $0.overline001122334455667789$. (But cute nonetheless!)
    – John
    3 hours ago













  • 4




    $1/891$ isn't quite all that: $0.overline001122334455667789$. (But cute nonetheless!)
    – John
    3 hours ago








4




4




$1/891$ isn't quite all that: $0.overline001122334455667789$. (But cute nonetheless!)
– John
3 hours ago





$1/891$ isn't quite all that: $0.overline001122334455667789$. (But cute nonetheless!)
– John
3 hours ago











2 Answers
2






active

oldest

votes

















up vote
4
down vote













$$frac15=0.001100110011ldots_2;,$$



$$frac110=0.001100110011ldots_3;,$$



and generally



$$frac1101=0.001100110011ldots$$



in all bases.






share|cite|improve this answer






















  • This one crosses over from cute to beautiful.
    – John
    2 hours ago

















up vote
1
down vote













$$frac22449999=0.overline2244$$
$$frac2244668810^8-1=0.overline22446688$$
$$frac11223344556677889910^18-1=0.overline112233445566778899$$
$$frac2909=0.overline0022$$
$$frac11339999=0.overline1133$$



$$frac111=0.overline09$$






share|cite|improve this answer






















  • Cool-looking ... but the only doubled digit I see is $11$.
    – John
    2 hours ago










  • okay I removed the other two examples
    – Deepesh Meena
    2 hours ago










  • I tried to create some examples using old-school math trick :P
    – Deepesh Meena
    1 hour ago










  • But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
    – Michael Hardy
    24 mins ago










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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
4
down vote













$$frac15=0.001100110011ldots_2;,$$



$$frac110=0.001100110011ldots_3;,$$



and generally



$$frac1101=0.001100110011ldots$$



in all bases.






share|cite|improve this answer






















  • This one crosses over from cute to beautiful.
    – John
    2 hours ago














up vote
4
down vote













$$frac15=0.001100110011ldots_2;,$$



$$frac110=0.001100110011ldots_3;,$$



and generally



$$frac1101=0.001100110011ldots$$



in all bases.






share|cite|improve this answer






















  • This one crosses over from cute to beautiful.
    – John
    2 hours ago












up vote
4
down vote










up vote
4
down vote









$$frac15=0.001100110011ldots_2;,$$



$$frac110=0.001100110011ldots_3;,$$



and generally



$$frac1101=0.001100110011ldots$$



in all bases.






share|cite|improve this answer














$$frac15=0.001100110011ldots_2;,$$



$$frac110=0.001100110011ldots_3;,$$



and generally



$$frac1101=0.001100110011ldots$$



in all bases.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 2 hours ago

























answered 2 hours ago









joriki

167k10180333




167k10180333











  • This one crosses over from cute to beautiful.
    – John
    2 hours ago
















  • This one crosses over from cute to beautiful.
    – John
    2 hours ago















This one crosses over from cute to beautiful.
– John
2 hours ago




This one crosses over from cute to beautiful.
– John
2 hours ago










up vote
1
down vote













$$frac22449999=0.overline2244$$
$$frac2244668810^8-1=0.overline22446688$$
$$frac11223344556677889910^18-1=0.overline112233445566778899$$
$$frac2909=0.overline0022$$
$$frac11339999=0.overline1133$$



$$frac111=0.overline09$$






share|cite|improve this answer






















  • Cool-looking ... but the only doubled digit I see is $11$.
    – John
    2 hours ago










  • okay I removed the other two examples
    – Deepesh Meena
    2 hours ago










  • I tried to create some examples using old-school math trick :P
    – Deepesh Meena
    1 hour ago










  • But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
    – Michael Hardy
    24 mins ago














up vote
1
down vote













$$frac22449999=0.overline2244$$
$$frac2244668810^8-1=0.overline22446688$$
$$frac11223344556677889910^18-1=0.overline112233445566778899$$
$$frac2909=0.overline0022$$
$$frac11339999=0.overline1133$$



$$frac111=0.overline09$$






share|cite|improve this answer






















  • Cool-looking ... but the only doubled digit I see is $11$.
    – John
    2 hours ago










  • okay I removed the other two examples
    – Deepesh Meena
    2 hours ago










  • I tried to create some examples using old-school math trick :P
    – Deepesh Meena
    1 hour ago










  • But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
    – Michael Hardy
    24 mins ago












up vote
1
down vote










up vote
1
down vote









$$frac22449999=0.overline2244$$
$$frac2244668810^8-1=0.overline22446688$$
$$frac11223344556677889910^18-1=0.overline112233445566778899$$
$$frac2909=0.overline0022$$
$$frac11339999=0.overline1133$$



$$frac111=0.overline09$$






share|cite|improve this answer














$$frac22449999=0.overline2244$$
$$frac2244668810^8-1=0.overline22446688$$
$$frac11223344556677889910^18-1=0.overline112233445566778899$$
$$frac2909=0.overline0022$$
$$frac11339999=0.overline1133$$



$$frac111=0.overline09$$







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 1 hour ago

























answered 2 hours ago









Deepesh Meena

3,4102824




3,4102824











  • Cool-looking ... but the only doubled digit I see is $11$.
    – John
    2 hours ago










  • okay I removed the other two examples
    – Deepesh Meena
    2 hours ago










  • I tried to create some examples using old-school math trick :P
    – Deepesh Meena
    1 hour ago










  • But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
    – Michael Hardy
    24 mins ago
















  • Cool-looking ... but the only doubled digit I see is $11$.
    – John
    2 hours ago










  • okay I removed the other two examples
    – Deepesh Meena
    2 hours ago










  • I tried to create some examples using old-school math trick :P
    – Deepesh Meena
    1 hour ago










  • But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
    – Michael Hardy
    24 mins ago















Cool-looking ... but the only doubled digit I see is $11$.
– John
2 hours ago




Cool-looking ... but the only doubled digit I see is $11$.
– John
2 hours ago












okay I removed the other two examples
– Deepesh Meena
2 hours ago




okay I removed the other two examples
– Deepesh Meena
2 hours ago












I tried to create some examples using old-school math trick :P
– Deepesh Meena
1 hour ago




I tried to create some examples using old-school math trick :P
– Deepesh Meena
1 hour ago












But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
– Michael Hardy
24 mins ago




But here you're putting the doubling of the digits into the input by design, so that's not as good. And similarly with "joriki" 's examples.
– Michael Hardy
24 mins ago

















 

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