A138837 -id:A138837 - cp's OEIS frontend

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

Omar E. Pol, Apr 05 2008

nonn

Numbers that are not in A001348.

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

Chai Wah Wu, Algorithms for complementary sequences, arXiv:2409.05844 [math.NT], 2024.

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

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

A138889 Primes that are not Fermat primes.

Original entry on oeis.org

2, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269, 271, 277, 281, 283

Offset: 1

Omar E. Pol, Apr 03 2008

Primes that are not members of A019434.

Cf. A000040, A000217, A019434, A138837, A138888.

A218582 Primes which do not divide any Mersenne number M(p) = 2^p - 1 with prime p.

Original entry on oeis.org

2, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199, 211, 227, 229, 239, 241, 251, 257, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset: 1

Arkadiusz Wesolowski, Nov 03 2012

nonn

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Complement in primes of A122094. Subsequence of A138837.

[p: p in PrimesInInterval(2, 337) | not IsPrime(Modorder(2, p))];

Select[Prime@Range[68], ! PrimeQ@MultiplicativeOrder[2, #] &]

A340466 Primes whose binary expansion contains more 1's than 0's but at least one 0.

Original entry on oeis.org

5, 11, 13, 19, 23, 29, 43, 47, 53, 59, 61, 71, 79, 83, 89, 101, 103, 107, 109, 113, 151, 157, 167, 173, 179, 181, 191, 199, 211, 223, 227, 229, 233, 239, 241, 251, 271, 283, 307, 311, 313, 317, 331, 347, 349, 359, 367, 373, 379, 383, 397, 409, 419, 421, 431

Offset: 1

Ctibor O. Zizka, Jan 08 2021

			71 is in the sequence because 71 is a prime and 71_10 = 1000111_2. '1000111' has four 1's and three 0's.

Cf. A000040, A000225, A000668, A066196, A095070, A095071, A138837.

Select[Range[400], PrimeQ[#] && First[d = DigitCount[#, 2]] > Last[d] > 0 &] (* Amiram Eldar, Jan 08 2021 *)

isok(n) = if (isprime(n), my(nb=#binary(n), h=hammingweight(n)); (2*h > nb) && (h < nb)); \\ Michel Marcus, Jan 10 2021

from sympy import sieve
A340466_list = [p for p in sieve.primerange(1,10**4) if len(bin(p))-2 < 2*bin(p).count('1') < 2*len(bin(p))-4] # Chai Wah Wu, Jan 10 2021

{ A095070 } minus { A000225 }.
{ A095070 } minus { A000668 }.
{ A095070 } intersect { A138837 }.

cp's OEIS Frontend

A138836 Non-Mersenne numbers A001348.

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A138889 Primes that are not Fermat primes.

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A218582 Primes which do not divide any Mersenne number M(p) = 2^p - 1 with prime p.

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A340466 Primes whose binary expansion contains more 1's than 0's but at least one 0.

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