A077372 -id:A077372 - cp's OEIS frontend

A077371 Fibonacci numbers whose internal digits form a Fibonacci number. Equivalently, Fibonacci numbers from which deleting the MSD and LSD leaves a Fibonacci number.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 233, 610, 987

Offset: 1

Amarnath Murthy, Nov 06 2002

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)

Manfred Scheucher, Sage Script

Cf. A077372, A077373, A077374, A077375.

A077373 Fibonacci numbers whose external digits as well as internal digits form a Fibonacci number.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

Offset: 1

Amarnath Murthy, Nov 06 2002

Conjecture: sequence is finite. Is there any term > 89 in this sequence?

Tanya Khovanova, Non Recursions

Intersection of A077371 and A077372.

cp's OEIS Frontend

A077371 Fibonacci numbers whose internal digits form a Fibonacci number. Equivalently, Fibonacci numbers from which deleting the MSD and LSD leaves a Fibonacci number.

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