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Does every seed for a Fibonacci Sequence generate exactly one square? [on hold]
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If you start with any two integers, add them, then add the sum to the second, then add that sum to the first sum, etc, making a Fibonacci sequence from the first two numbers. Is it guaranteed to be exactly one square number in the generated sequence? Is there any corollary to the tribonacci, etc.
number-theory fibonacci-numbers
edited Sep 9 at 0:53
peterh
2,15441631
asked Sep 8 at 23:24
William Grannis
792418
put on hold as off-topic by user21820, user91500, Jendrik Stelzner, Learnmore, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, user91500, Jendrik Stelzner, Learnmore, John Ma
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up vote
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If you start with any two integers, add them, then add the sum to the second, then add that sum to the first sum, etc, making a Fibonacci sequence from the first two numbers. Is it guaranteed to be exactly one square number in the generated sequence? Is there any corollary to the tribonacci, etc.
number-theory fibonacci-numbers
edited Sep 9 at 0:53
peterh
2,15441631
asked Sep 8 at 23:24
William Grannis
792418
put on hold as off-topic by user21820, user91500, Jendrik Stelzner, Learnmore, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, user91500, Jendrik Stelzner, Learnmore, John Ma
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If you start with any two integers, add them, then add the sum to the second, then add that sum to the first sum, etc, making a Fibonacci sequence from the first two numbers. Is it guaranteed to be exactly one square number in the generated sequence? Is there any corollary to the tribonacci, etc.
number-theory fibonacci-numbers
edited Sep 9 at 0:53
peterh
2,15441631
asked Sep 8 at 23:24
William Grannis
792418
If you start with any two integers, add them, then add the sum to the second, then add that sum to the first sum, etc, making a Fibonacci sequence from the first two numbers. Is it guaranteed to be exactly one square number in the generated sequence? Is there any corollary to the tribonacci, etc.
number-theory fibonacci-numbers
number-theory fibonacci-numbers
edited Sep 9 at 0:53
peterh
2,15441631
asked Sep 8 at 23:24
William Grannis
792418
edited Sep 9 at 0:53
peterh
2,15441631
asked Sep 8 at 23:24
William Grannis
792418
edited Sep 9 at 0:53
peterh
2,15441631
edited Sep 9 at 0:53
peterh
2,15441631
edited Sep 9 at 0:53
peterh
2,15441631
2,15441631
asked Sep 8 at 23:24
William Grannis
792418
asked Sep 8 at 23:24
William Grannis
792418
asked Sep 8 at 23:24
William Grannis
792418
792418
put on hold as off-topic by user21820, user91500, Jendrik Stelzner, Learnmore, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, user91500, Jendrik Stelzner, Learnmore, John Ma
put on hold as off-topic by user21820, user91500, Jendrik Stelzner, Learnmore, John Ma 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, user91500, Jendrik Stelzner, Learnmore, John Ma
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3 Answers
3
active
oldest
votes
up vote
14
down vote
accepted
Starting with $2$ and $7$ you get the sequence $2,7,9,16,25,cdots$
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
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up vote
10
down vote
Just double the standard Fibonacci sequence:
2, 2, 4, 6, 10, 16, ... .
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
1
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
add a comment |Â
up vote
9
down vote
Take any two square numbers as your seed. Now you have a sequence with two square numbers.
answered Sep 8 at 23:53
Théophile
17.1k12438
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
5
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
1
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
14
down vote
accepted
Starting with $2$ and $7$ you get the sequence $2,7,9,16,25,cdots$
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
add a comment |Â
up vote
14
down vote
accepted
Starting with $2$ and $7$ you get the sequence $2,7,9,16,25,cdots$
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
add a comment |Â
up vote
14
down vote
accepted
up vote
14
down vote
accepted
Starting with $2$ and $7$ you get the sequence $2,7,9,16,25,cdots$
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
Starting with $2$ and $7$ you get the sequence $2,7,9,16,25,cdots$
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
answered Sep 8 at 23:31
Alessandro Codenotti
3,39211438
3,39211438
add a comment |Â
add a comment |Â
up vote
10
down vote
Just double the standard Fibonacci sequence:
2, 2, 4, 6, 10, 16, ... .
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
1
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
add a comment |Â
up vote
10
down vote
Just double the standard Fibonacci sequence:
2, 2, 4, 6, 10, 16, ... .
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
1
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
add a comment |Â
up vote
10
down vote
up vote
10
down vote
Just double the standard Fibonacci sequence:
2, 2, 4, 6, 10, 16, ... .
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
Just double the standard Fibonacci sequence:
2, 2, 4, 6, 10, 16, ... .
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
answered Sep 9 at 0:07
Oscar Lanzi
10.3k11733
10.3k11733
1
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
add a comment |Â
1
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
1
1
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
Why the deletion vote please?
– Oscar Lanzi
Sep 9 at 1:07
add a comment |Â
up vote
9
down vote
Take any two square numbers as your seed. Now you have a sequence with two square numbers.
answered Sep 8 at 23:53
Théophile
17.1k12438
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
5
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
1
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
add a comment |Â
up vote
9
down vote
Take any two square numbers as your seed. Now you have a sequence with two square numbers.
answered Sep 8 at 23:53
Théophile
17.1k12438
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
5
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
1
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
add a comment |Â
up vote
9
down vote
up vote
9
down vote
Take any two square numbers as your seed. Now you have a sequence with two square numbers.
answered Sep 8 at 23:53
Théophile
17.1k12438
Take any two square numbers as your seed. Now you have a sequence with two square numbers.
answered Sep 8 at 23:53
Théophile
17.1k12438
answered Sep 8 at 23:53
Théophile
17.1k12438
answered Sep 8 at 23:53
Théophile
17.1k12438
answered Sep 8 at 23:53
Théophile
17.1k12438
17.1k12438
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
5
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
1
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
add a comment |Â
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
5
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
1
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
I assumed the seeds are not to be counted, otherwise even the usual sequence has two squares as seeds!
– Alessandro Codenotti
Sep 8 at 23:55
5
5
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
@AlessandroCodenotti Ah, but in that case, just count backwards as many times as you like to generate earlier seeds for essentially the same sequence. (Starting with $9, 16$, we can count backwards to get your example, which is maybe how you chose it yourself?)
– Théophile
Sep 9 at 0:42
1
1
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
@Théopile that's how I found it, indeed!
– Alessandro Codenotti
Sep 9 at 7:21
add a comment |Â
