A032356 -id:A032356 - cp's OEIS frontend

A300406 Primes of the form 13*2^n + 1.

53, 3329, 13313, 13631489, 3489660929, 62864142619960717084721153, 5100145160001678120616578906356228963083163798627028041729, 6779255729241169695101387251026410519979286814120235842117075415451380965612384558178346467329, 1735489466685739441945955136262761093114697424414780375581971306355553527196770446893656695635969

Offset: 1

Martin Renner, Mar 05 2018

nonn

For the corresponding exponents n see A032356.

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

Cf. A019434, A039687, A032356, A050527, A050528, A050529, A173236, A195745, A050526, A300407, A300408.

Filtered(List([1..500],n->13*2^n + 1),IsPrime); # Muniru A Asiru, Mar 06 2018

[a: n in [1..400] | IsPrime(a) where a is 13*2^n + 1]; // Vincenzo Librandi, Mar 06 2018

a:=(n,k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n,13), n=1..316);

Select[Table[13 2^n + 1, {n, 400}], PrimeQ] (* Vincenzo Librandi, Mar 06 2018 *)

lista(nn) = {for(k=1, nn, if(ispseudoprime(p=13*2^k+1), print1(p, ", ")));} \\ Altug Alkan, Mar 29 2018

a(n) = A168596(A032356(n)). - Michel Marcus, Mar 29 2018

A001773 Numbers k such that 13*2^k - 1 is prime.

Original entry on oeis.org

3, 7, 23, 287, 291, 795, 2203, 5711, 7927, 9443, 10095, 19071, 29611, 34651, 51875, 55343, 77511, 166303, 233207

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).

Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
Wilfrid Keller, List of primes k.2^n - 1 for 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. A032356 (13*2^k+1 is prime).

is(n)=ispseudoprime(13*2^n-1) \\ Charles R Greathouse IV, May 22 2017

More terms from Hugo Pfoertner, Jun 23 2004

A002257 Numbers k such that 13*4^k + 1 is prime.

Original entry on oeis.org

1, 4, 5, 10, 14, 41, 94, 154, 158, 500, 14140, 19004, 21928, 44009, 54629, 57148, 260653, 281228, 342280, 519448, 749938, 930866

Offset: 1

N. J. A. Sloane

H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, 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).

Ray Ballinger, Proth Search Page.
R. M. Robinson, A report on primes of the form k.2^n+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc., 9 (1958), 673-681.

See A032356 (n such that 13*2^n+1 is prime) for more terms.

[ k: k in [1..800]|IsPrime(13*4^k+1)]; // Vincenzo Librandi, Nov 21 2010

Select[Range[2000],PrimeQ[13 4^#+1]&] (* Harvey P. Dale, Jan 22 2011 *)

for(k=1,10^5,if(ispseudoprime(13*4^k+1),print1(k, ", "))); /* Joerg Arndt, Apr 07 2013 */

Added more terms (from A032356), Joerg Arndt, Apr 07 2013

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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A300406 Primes of the form 13*2^n + 1.

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A001773 Numbers k such that 13*2^k - 1 is prime.

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A002257 Numbers k such that 13*4^k + 1 is 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.