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

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, 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, 9, 11, 9, 7, 7, 12, 10, 10, 9, 9, 9, 6, 11, 10, 11, 9, 12

Offset: 0

Author

Alois P. Heinz, Feb 17 2017

Keywords

• nonn

Examples

			a(1) = 1: {2}.
a(2) = 2: {1,2}, {2,3}.
a(3) = 1: {1,2,4}.
a(4) = 2: {1,2,3,5}, {1,3,4,5}.
a(5) = 2: {1,2,3,5,6}, {1,3,4,5,6}.
a(6) = 1: {1,2,3,4,6,7}.
a(7) = 2: {1,2,3,4,5,6,8}, {1,2,3,4,6,7,8}.
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}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A000720, A282516.

Similar but different: A065382, A066888, A090970.

Programs

Maple

a:= proc(n) option remember; (t-> add(`if`(isprime(
       t-i), 1, 0), i=1..n+1))((n+1)*(n+2)/2)
    end:
seq(a(n), n=0..100);

Formula

a(n) = A282516(n+1,n).

a(n) = pi((n+1)*(n+2)/2)-pi(n*(n+1)/2) for n >= 3, pi = A000720.