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%I #13 Jun 03 2015 19:33:38
%S 0,1,1,2,3,5,8,13,21,34,55,89,233,610,987
%N Fibonacci numbers whose internal digits form a Fibonacci number. Equivalently, Fibonacci numbers from which deleting the MSD and LSD leaves a Fibonacci number.
%C Conjecture: The sequence is finite.
%C No more terms < 10^6. - _Lars Blomberg_, May 20 2015
%C From _Manfred Scheucher_, Jun 02 2015 (Start)
%C No more terms < 10^10000.
%C 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).
%C 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.
%C The sequence seems to be finite for any base, not just for base 10.
%C 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.
%C (End)
%H Manfred Scheucher, <a href="/A077371/a077371.sage.txt">Sage Script</a>
%Y Cf. A077372, A077373, A077374, A077375.
%K base,more,nonn
%O 1,4
%A _Amarnath Murthy_, Nov 06 2002