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A282518 Number of n-element subsets of [n+1] having a prime element sum.

%I A282518 #10 Feb 20 2017 09:01:14
%S A282518 0,1,2,1,2,2,1,2,3,2,2,3,3,3,3,2,4,3,3,4,4,4,4,4,4,4,4,5,5,6,4,5,3,6,
%T A282518 6,7,5,5,6,4,8,5,6,6,8,6,8,5,7,5,11,4,6,9,7,8,9,8,7,7,9,7,8,7,12,5,9,
%U A282518 9,11,9,7,7,12,10,10,9,9,9,6,11,10,11,9,12
%N A282518 Number of n-element subsets of [n+1] having a prime element sum.
%H A282518 Alois P. Heinz, <a href="/A282518/b282518.txt">Table of n, a(n) for n = 0..20000</a>
%F A282518 a(n) = A282516(n+1,n).
%F A282518 a(n) = pi((n+1)*(n+2)/2)-pi(n*(n+1)/2) for n >= 3, pi = A000720.
%e A282518 a(1) = 1: {2}.
%e A282518 a(2) = 2: {1,2}, {2,3}.
%e A282518 a(3) = 1: {1,2,4}.
%e A282518 a(4) = 2: {1,2,3,5}, {1,3,4,5}.
%e A282518 a(5) = 2: {1,2,3,5,6}, {1,3,4,5,6}.
%e A282518 a(6) = 1: {1,2,3,4,6,7}.
%e A282518 a(7) = 2: {1,2,3,4,5,6,8}, {1,2,3,4,6,7,8}.
%e A282518 a(8) = 3: {1,2,3,4,5,6,7,9}, {1,2,3,5,6,7,8,9}, {1,3,4,5,6,7,8,9}.
%p A282518 a:= proc(n) option remember; (t-> add(`if`(isprime(
%p A282518        t-i), 1, 0), i=1..n+1))((n+1)*(n+2)/2)
%p A282518     end:
%p A282518 seq(a(n), n=0..100);
%Y A282518 Cf. A000720, A282516.
%Y A282518 Similar but different: A065382, A066888, A090970.
%K A282518 nonn
%O A282518 0,3
%A A282518 _Alois P. Heinz_, Feb 17 2017