

A282518


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


2



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
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OFFSET

0,3


LINKS

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


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.


EXAMPLE

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}.


MAPLE

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


CROSSREFS

Cf. A000720, A282516.
Similar but different: A065382, A066888, A090970.
Sequence in context: A067437 A242425 A263104 * A230241 A029315 A070080
Adjacent sequences: A282515 A282516 A282517 * A282519 A282520 A282521


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Feb 17 2017


STATUS

approved



