A177687 Number of distinct transpositions of digits (zeros and units) in n-th prime written in base 2.

2, 1, 3, 1, 4, 4, 10, 10, 5, 5, 1, 20, 20, 15, 6, 15, 6, 6, 35, 35, 35, 21, 35, 35, 35, 35, 21, 21, 21, 35, 1, 56, 56, 70, 70, 56, 56, 70, 56, 56, 56, 56, 8, 56, 70, 56, 56, 8, 56, 56, 56, 8, 56, 8, 36, 126, 126, 126, 126, 126, 126, 126, 126, 84, 126, 84, 126, 126, 84, 84, 126, 84

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = binomial((A000120(p) + A023416(p), A000120(p)), where p=prime(n). - R. J. Mathar, May 15 2010

a(n) = A178244(A000040(n)). - Robert Israel, Oct 25 2023

Example

a(1)=2 because 2 =  10_2 and |{10, 01}| = 2,
a(2)=1 because 3 =  11_2 and |{11}| = 1,
a(3)=3 because 5 = 101_2 and |{101, 011, 110}| = 3.

Maple

A177687 := proc(n) p := ithprime(n) ; combinat[numbperm](convert(p, base, 2)) ; end proc: seq(A177687(n), n=1..120) ; # R. J. Mathar, May 15 2010

Mathematica

Array[Length@ Permutations@ IntegerDigits[Prime@ #, 2] &, 72] (* Michael De Vlieger, Feb 15 2019 *)

Crossrefs

Cf. A004676, A168324, A178244.

Sequence in context: A142884 A347028 A325365 * A219356 A142878 A299774

Adjacent sequences: A177684 A177685 A177686 * A177688 A177689 A177690

Keyword

nonn,base,look

Author

Juri-Stepan Gerasimov, May 12 2010, May 14 2010

Extensions

Terms corrected by D. S. McNeil and R. J. Mathar, May 14 2010

Status

approved