A118956 Numbers that cannot be written as 2^k + p with p prime < 2^k.

1, 2, 3, 4, 5, 8, 9, 12, 14, 16, 17, 20, 22, 24, 25, 26, 28, 30, 31, 32, 33, 36, 38, 40, 41, 42, 44, 46, 47, 48, 50, 52, 53, 54, 56, 57, 58, 59, 60, 62, 64, 65, 68, 70, 72, 73, 74, 76, 78, 79, 80, 82, 84, 85, 86, 88, 89, 90, 91, 92, 94, 96, 97, 98, 99, 100, 102, 103, 104, 106

Offset

1,2

Comments

Complement of A118957.

A118954 is a subsequence.

Links

Table of n, a(n) for n=1..70.

Formula

A118952(a(n)) = 0.

Mathematica

nn=15; Complement[Range[nn^2], Flatten[Table[c=2^n; c+Prime[ Range[ PrimePi[ c]]], {n, 2, nn}]]] (* Harvey P. Dale, Sep 14 2012 *)

Prog

(Python)
from sympy import primepi
def A118956(n):
    def f(x): return int(n+sum(primepi(min(x-(m:=1<<k), m-1)) for k in range(x.bit_length())))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Feb 23 2025

Crossrefs

Cf. A118952, A118954, A118957.

Sequence in context: A242175 A325662 A275771 * A372586 A109850 A008749

Adjacent sequences: A118953 A118954 A118955 * A118957 A118958 A118959

Keyword

nonn

Author

Reinhard Zumkeller, May 07 2006

Status

approved