A272851 -id:A272851 - cp's OEIS frontend

A272852 Smallest value m such that A272851(m) = n.

1, 2, 5, 11, 13, 53, 418, 1698, 8887, 54882, 455445, 7287129, 116594064

Offset: 1

Marko Riedel, May 07 2016

Marko Riedel, C program to compute sequence.
Marko Riedel, C program to compute sequence, not assuming all smaller values appear before larger ones.

s = Fibonacci@ Range@ 120; Function[k, FirstPosition[k, #] & /@ Range@ Max@ k]@ Table[Length@ Select[Union@ Flatten@ Function[k, Map[FromDigits[#, 2] & /@ Partition[k, #, 1] &, Range@ Length@ k]]@IntegerDigits[#, 2] &@ n, MemberQ[s, #] &], {n, 10^4}] // Flatten (* Michael De Vlieger, May 08 2016, Version 10 *)

A272886 Number of distinct Fibonacci numbers among the contiguous substrings of the binary digits of n.

Original entry on oeis.org

1, 3, 2, 3, 4, 4, 2, 4, 3, 4, 5, 4, 6, 4, 2, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 6, 6, 4, 6, 4, 2, 4, 4, 5, 5, 3, 4, 4, 4, 5, 4, 5, 6, 5, 6, 5, 5, 5, 5, 4, 4, 6, 7, 6, 7, 5, 4, 6, 6, 4, 6, 4, 2, 4, 4, 4, 5, 5, 6, 5, 5, 4, 3, 4, 5, 4, 6, 4, 4, 5, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 5, 6, 5, 5, 5

Offset: 1

Marko Riedel, May 08 2016

nonn

			a(53) = 7 because 53=(110101)_2 which contains (0)_2 = 0, (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 as do two and zero.

Marko Riedel, Maple program to compute sequence.

Cf. A000045, A078822, A272851, A272852.

A269502 Number of contiguous substrings of the binary representation of n that are equal to some a(m) where 1 <= m < n and where a(1)=1.

Original entry on oeis.org

1, 1, 2, 2, 4, 3, 5, 3, 6, 7, 8, 6, 8, 8, 9, 4, 8, 10, 11, 10, 12, 12, 13, 8, 11, 12, 13, 10, 12, 11, 12, 4, 9, 12, 13, 13, 15, 15, 16, 12, 15, 16, 17, 15, 17, 15, 18, 9, 13, 15, 15, 14, 16, 16, 17, 12, 15, 16, 17, 15

Offset: 1

Marko Riedel, May 11 2016

			a(7) = 5 because 7 = (111)_2 and (1)_2 occurs three times and (11)_2 two times; (111)_2 does not occur among a(1) ... a(6).

Marko Riedel, Maple program for A269502 and A272976.

Cf. A272886, A272851, A272976.

cp's OEIS Frontend

A272852 Smallest value m such that A272851(m) = n.

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A272886 Number of distinct Fibonacci numbers among the contiguous substrings of the binary digits of n.

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A269502 Number of contiguous substrings of the binary representation of n that are equal to some a(m) where 1 <= m < n and where a(1)=1.

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Author

Keywords

Examples

Links

Crossrefs