OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..3830
FORMULA
EXAMPLE
a(5)=12 subsets of {1,2,3,4,5} contain exactly two primes: {2,3}, {2,5}, {3,5}, {1,2,3}, {1,2,5}, {1,3,5}, {2,3,4}, {2,4,5}, {3,4,5}, {1,2,3,4}, {1,2,4,5} and {1,3,4,5}.
MAPLE
N:= 100: # for a(1)..a(N)
V:= Vector(N):
p:= 1: n:= 1: pi:= 0:
while n <= N do
p:= nextprime(p);
for n from n to min(N, p-1) do
V[n]:= pi*(pi-1)*2^(n-pi)/2;
od;
pi:= pi+1;
n:= p;
od:
convert(V, list); # Robert Israel, Jul 14 2019
# second Maple program:
b:= proc(n, c) option remember; `if`(n=0, `if`(c=0, 1, 0),
`if`(c<0, 0, b(n-1, c)+b(n-1, c-`if`(isprime(n), 1, 0))))
end:
a:= n-> b(n, 2):
seq(a(n), n=1..42); # Alois P. Heinz, Dec 19 2019
MATHEMATICA
b[n_, c_] := b[n, c] = If[n == 0, If[c == 0, 1, 0], If[c < 0, 0, b[n-1, c] + b[n-1, c - If[PrimeQ[n], 1, 0]]]];
a[n_] := b[n, 2];
Array[a, 42] (* Jean-François Alcover, May 30 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 12 2003
STATUS
approved