A002261 -id:A002261 - cp's OEIS frontend

A050529 Primes of the form 11*2^k + 1.

23, 89, 353, 1409, 5767169, 23068673, 96757023244289, 26596368031521841843535873, 467888254516290387262140085218681290753, 1871553018065161549048560340874725163009, 9050275065266633231852330504065427777405047260984689248417349633

Offset: 1

N. J. A. Sloane, Dec 29 1999

nonn

For more terms see A002261.

Cf. A083683.

Select[11*2^Range[210]+1,PrimeQ] (* Harvey P. Dale, Jun 15 2017 *)

a(n) = A083683(A002261(n)). - Elmo R. Oliveira, May 04 2025

A001772 Numbers k such that 11*2^k - 1 is prime.

Original entry on oeis.org

2, 26, 50, 54, 126, 134, 246, 354, 362, 950, 1310, 2498, 6926, 11826, 31734, 67850, 74726, 96150, 374114, 696438, 743322, 1044086, 1104606, 1261478

Offset: 1

N. J. A. Sloane

H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Kosmaj, Riesel list k<300.
H. C. Williams and C. R. Zarnke, A report on prime numbers of the forms M = (6a+1)*2^(2m-1)-1 and (6a-1)*2^(2m)-1, Math. Comp., 22 (1968), 420-422.
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A050525.

Cf. A002261 (11*2^k+1 is prime).

is(n)=ispseudoprime(11*2^n-1) \\ Charles R Greathouse IV, Feb 20 2017

from sympy import isprime
def aupto(lim): return [k for k in range(1, lim+1) if isprime(11*2**k - 1)]
print(aupto(2500)) # Michael S. Branicky, Feb 26 2021

More terms from Hugo Pfoertner, Jun 23 2004

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

A322302 Primes p such that 11*2^p + 1 is also prime.

Original entry on oeis.org

3, 5, 7, 19, 43, 127, 211, 15329, 28277, 3771821

Offset: 1

Vincenzo Librandi, Dec 20 2018

Primes in A002261.

Cf. A002261, A175172.

Filtered([1..1000], p -> IsPrime(p) and IsPrime(11*2^p+1)); # Muniru A Asiru, Dec 20 2018

[p: p in PrimesUpTo (6000) | IsPrime(11*2^p+1)];

select(p->isprime(p) and isprime(11*2^p+1),[$1..1000]); # Muniru A Asiru, Dec 20 2018

Select[Prime[Range[1000]], PrimeQ[11 2^# + 1] &]

a(10) from Joerg Arndt Dec 20 2018

A361076 Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2n-1)2^k+1, if they exist and n > 1; and of zeros otherwise.

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 2, 3, 5, 8, 1, 4, 7, 6, 16, 1, 2, 6, 13, 8, 32, 2, 3, 3, 14, 15, 12, 64, 1, 8, 5, 6, 20, 25, 18, 128, 3, 2, 10, 7, 7, 26, 39, 30, 256, 6, 15, 4, 20, 19, 11, 50, 55, 36, 512, 1, 10, 27, 9, 28, 21, 14, 52, 75, 41, 1024, 1, 4, 46, 51, 10, 82, 43, 17, 92, 85, 66, 2048

Offset: 1

Lorenzo Sauras Altuzarra, Mar 01 2023

Is a(n) <= A279709(n)?

			Table starts
  1   2   4   8  16  32  64 128 ... A000079
  1   2   5   6   8  12  18  30 ... A002253
  1   3   7  13  15  25  39  55 ... A002254
  2   4   6  14  20  26  50  52 ... A032353
  1   2   3   6   7  11  14  17 ... A002256
  1   3   5   7  19  21  43  81 ... A002261
  2   8  10  20  28  82 188 308 ... A032356
  1   2   4   9  10  12  27  37 ... A002258
  ...
(2*39279 - 1)*2^r + 1 is composite for every r > 0 (see comments from A046067), so the 39279th row is A000004, the zero sequence.

Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300.

Cf. A000079, A002253, A002254, A032353, A002256, A002261, A032356, A002258.
Cf. A033809 (1st column).
Cf. A000004, A046067, A279709.

vk(k, nn) = if (k==1, return (vector(nn, i, 2^(i-1)))); my(v = vector(nn-k+1), nb=0, i=0, x); while (nb != nn-k+1, if (isprime((2*k-1)*2^i+1), nb++; v[nb] = i); i++;); v;
lista(nn) = my(v=vector(nn, k, vk(k, nn))); my(w=List()); for (i=1, nn, for (j=1, i, listput(w, v[i-j+1][j]););); Vec(w); \\ Michel Marcus, Mar 03 2023

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A050529 Primes of the form 11*2^k + 1.

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A001772 Numbers k such that 11*2^k - 1 is prime.

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A322302 Primes p such that 11*2^p + 1 is also prime.

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A361076 Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.

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PARI

A361076 Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2n-1)2^k+1, if they exist and n > 1; and of zeros otherwise.