A369853 a(n) = number of subsets S of {1,2,...,n} such that (number of nonprimes in S) < (number of primes in S).

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

0,5

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A224915 A135301 A294175 * A370337 A192917 A030672

Adjacent sequences: A369850 A369851 A369852 * A369854 A369855 A369856

Keyword

nonn

Author

Clark Kimberling, Feb 03 2024

Extensions

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

Status

approved