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 A272851 Number of distinct nonzero Fibonacci numbers among the contiguous substrings of the binary digits of n. 4
 1, 2, 2, 2, 3, 3, 2, 3, 2, 3, 4, 3, 5, 3, 2, 3, 3, 2, 3, 3, 4, 4, 4, 4, 3, 5, 5, 3, 5, 3, 2, 3, 3, 4, 4, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 4, 4, 4, 4, 3, 3, 5, 6, 5, 6, 4, 3, 5, 5, 3, 5, 3, 2, 3, 3, 3, 4, 4, 5, 4, 4, 3, 2, 3, 4, 3, 5, 3, 3, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..80. Marko Riedel, Maple program to compute sequence. EXAMPLE a(53) = 6 because 53=(110101)_2 which contains (1)_2 = 1, (10)_2 = 2, (11)_2 = 3, (101)_2 = 5, (1101)_2 = 13 and (10101)_2 = 21. The one digit only contributes once. MATHEMATICA s = Fibonacci@ Range@ 30; Table[Length@ Select[Union@ Flatten@ Function[k, Map[FromDigits[#, 2] & /@ Partition[k, #, 1] &, Range@ Length@ k]]@IntegerDigits[#, 2] &@ n, MemberQ[s, #] &], {n, 120}] (* Michael De Vlieger, May 08 2016 *) PROG (PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8)) ; a(n) = {vb = binary(n); vf = []; for (i=1, #vb, for (j=1, #vb - i + 1, pvb = vector(j, k, vb[i+k-1]); f = subst(Pol(pvb), x, 2); if (f && isfib(f), vf = Set(concat(vf, f))); ); ); #vf; } \\ Michel Marcus, May 08 2016 CROSSREFS Cf. A000045, A078822, A272852, A272886. Sequence in context: A361088 A165924 A212628 * A242258 A232615 A257177 Adjacent sequences: A272848 A272849 A272850 * A272852 A272853 A272854 KEYWORD nonn,base AUTHOR Marko Riedel, May 07 2016 STATUS approved

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Last modified October 1 13:59 EDT 2023. Contains 365826 sequences. (Running on oeis4.)