A138836 Non-Mersenne numbers A001348.

1, 2, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

1,2

Comments

Numbers that are not in A001348.

a(1) to a(2042) equals A133398, then a(2043)=2048 <> A133398(2043)=2047.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Chai Wah Wu, Algorithms for complementary sequences, arXiv:2409.05844 [math.NT], 2024. See also Integers (2025) Vol. 25, Art. No. A95. See p. 24.

Mathematica

Complement[Range[Last[#] + 1], #] &@ Table[2^Prime[n] - 1, {n, 4}] (* Michael De Vlieger, Nov 06 2025 *)

Prog

(Python)
from sympy import primepi, prime
def A138836(n): return n+(k:=int(primepi((n).bit_length())-1))+int(n+k+1>=1<<prime(k+1)) if n>1 else 1 # Chai Wah Wu, Sep 10 2024

Crossrefs

Cf. A001348, A001690, A062289, A133398, A138837, A138888, A138890, A138891. A133398.

Sequence in context: A248962 A323455 A133398 * A175431 A387728 A059921

Adjacent sequences: A138833 A138834 A138835 * A138837 A138838 A138839

Keyword

nonn

Author

Omar E. Pol, Apr 05 2008

Status

approved