A077373 -id:A077373 - 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.

A077372 Fibonacci numbers whose external digits form a Fibonacci number. Or Fibonacci numbers whose MSD and LSD form a Fibonacci number.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 121393, 1836311903, 2504730781961, 10610209857723, 10284720757613717413913, 184551825793033096366333, 59425114757512643212875125, 155576970220531065681649693

Offset: 1

Amarnath Murthy, Nov 06 2002

Sequence can be easily generated up to >10000 terms with the appended Sage script. - Manfred Scheucher, Jun 02 2015

Manfred Scheucher, Table of n, a(n) for n = 1..100
Manfred Scheucher, Sage Script

Cf. A077371, A077373.

F=[fibonacci(i) for i in [0..200]]
[x for x in F if x<10 or (x>10 and (10*x.digits()[-1]+x.digits()[0]) in F)]
# Tom Edgar, Jun 03 2015

More terms from Lior Manor, Nov 06 2002

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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