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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