A369853 a(n) = number of subsets of {1,2,...,n} that contain more nonprimes than primes.

0, 1, 1, 1, 5, 6, 22, 29, 93, 256, 638, 1024, 2510, 4096, 9908, 22819, 50643, 89846, 199140, 354522, 784626, 1695222, 3593934, 6690448, 14198086, 29703676, 61450327, 126025204, 256737233, 500351356, 1020732722, 1986838144, 4058348603, 8245721686, 16684980092

Offset: 0

Author

Clark Kimberling, Feb 03 2024

Keywords

• nonn

Examples

			a(4) = 5 enumerates these subsets: {1}, {4}, {1,4}, {1,2,4}, {1,3,4}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000040, A018252, A369780, A369781, A369854.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, `if`(t<0, 1, 0),
      b(n-1, t)+b(n-1, t+`if`(isprime(n), 1, -1)))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..34);  # Alois P. Heinz, Feb 03 2024

Mathematica

Map[Length[Select[Map[Commonest, PrimeQ[Rest[Subsets[Range[#]]]]], # == {False, True} || # == {True, False} &]] &, Range[22]]   (* Peter J. C. Moses, Jan 29 2024 *)

Formula

a(n) = A369781(n) - A369854(n).

Extensions

a(23)-a(34) from Alois P. Heinz, Feb 03 2024