[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A077371
Fibonacci numbers whose internal digits form a Fibonacci number. Equivalently, Fibonacci numbers from which deleting the MSD and LSD leaves a Fibonacci number.
3
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 233, 610, 987
OFFSET
1,4
COMMENTS
Conjecture: The sequence is finite.
No more terms < 10^6. - Lars Blomberg, May 20 2015
From Manfred Scheucher, Jun 02 2015 (Start)
No more terms < 10^10000.
When considering binary representations, the sequence would be 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 144, and no further terms < 2^150000 (about 10^44095).
When considering k-ary representations with k=2..100, each of the sequences has some small terms in the beginning (as in the 10-ary case) and no further terms <10^1000.
The sequence seems to be finite for any base, not just for base 10.
Another observation: When considering k-ary representations with k=55,144,377,... (Fibonacci numbers with even index, A001906), the number of "initial terms" (terms <10^1000) increases very fast.
(End)
LINKS
CROSSREFS
KEYWORD
base,more,nonn
AUTHOR
Amarnath Murthy, Nov 06 2002
STATUS
approved