login
A282518
Number of n-element 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
OFFSET
0,3
LINKS
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(
t-i), 1, 0), i=1..n+1))((n+1)*(n+2)/2)
end:
seq(a(n), n=0..100);
CROSSREFS
Similar but different: A065382, A066888, A090970.
Sequence in context: A067437 A242425 A263104 * A230241 A029315 A070080
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 17 2017
STATUS
approved