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

%I A177687 #22 Oct 13 2024 19:43:59
%S A177687 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,
%T A177687 21,21,35,1,56,56,70,70,56,56,70,56,56,56,56,8,56,70,56,56,8,56,56,56,
%U A177687 8,56,8,36,126,126,126,126,126,126,126,126,84,126,84,126,126,84,84,126,84
%N A177687 Number of distinct transpositions of digits (zeros and units) in n-th prime written in base 2.
%H A177687 Robert Israel, <a href="/A177687/b177687.txt">Table of n, a(n) for n = 1..10000</a>
%F A177687 a(n) = binomial(A000120(p) + A023416(p), A000120(p)), where p=prime(n). - _R. J. Mathar_, May 15 2010
%F A177687 a(n) = A178244(A000040(n)). - _Robert Israel_, Oct 25 2023
%e A177687 a(1)=2 because 2 =  10_2 and |{10, 01}| = 2,
%e A177687 a(2)=1 because 3 =  11_2 and |{11}| = 1,
%e A177687 a(3)=3 because 5 = 101_2 and |{101, 011, 110}| = 3.
%p A177687 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
%t A177687 Array[Length@ Permutations@ IntegerDigits[Prime@ #, 2] &, 72] (* _Michael De Vlieger_, Feb 15 2019 *)
%Y A177687 Cf. A004676, A168324, A178244.
%K A177687 nonn,base,look,easy
%O A177687 1,1
%A A177687 _Juri-Stepan Gerasimov_, May 12 2010, May 14 2010
%E A177687 Terms corrected by _D. S. McNeil_ and _R. J. Mathar_, May 14 2010