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

Author

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

Keywords

• nonn
• base
• look
• easy

Examples

			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.
		

Links

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

Crossrefs

Cf. A004676, A168324, A178244.

Programs

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 *)

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

Extensions

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