

A286710


Numbers n whose Zeckendorf representation is of the form ww, for w a nonempty block of digits.


0



7, 16, 39, 54, 97, 120, 134, 246, 282, 304, 340, 376, 631, 688, 723, 780, 837, 872, 929, 964, 1631, 1722, 1778, 1869, 1960, 2016, 2107, 2163, 2254, 2345, 2401, 2492, 2583, 4236, 4382, 4472, 4618, 4764, 4854, 5000, 5090, 5236, 5382, 5472, 5618, 5764, 5854, 6000, 6090, 6236, 6382, 6472, 6618, 6708, 11035, 11270, 11415
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OFFSET

1,1


COMMENTS

The Zeckendorf representation of an integer n expresses n as a sum of nonadjacent Fibonacci numbers. It can be expressed as a word over {0,1} giving the coefficients, starting with the most significant digit.


LINKS

Table of n, a(n) for n=1..57.


EXAMPLE

The representation of 7 is 1010, which is of the form ww with w = 10.


MATHEMATICA

Reap[Do[ w = IntegerDigits[k, 2]; p = 1 + Flatten@ Position[ Reverse@ Join[w, w], 1]; If[ Min@ Differences@ p > 1, Sow@ Total@ Fibonacci@ p], {k, 2^10  1}]][[2, 1]] (* Giovanni Resta, May 13 2017 *)


CROSSREFS

Cf. A014417, A094202 (the same sequence, but for palindromes).
Sequence in context: A176449 A278945 A169877 * A036834 A020941 A318750
Adjacent sequences: A286707 A286708 A286709 * A286711 A286712 A286713


KEYWORD

nonn,base


AUTHOR

Jeffrey Shallit, May 13 2017


STATUS

approved



