A032353 -id:A032353 - cp's OEIS frontend

A050527 Primes of form 7*2^n+1.

29, 113, 449, 114689, 7340033, 469762049, 7881299347898369, 31525197391593473, 34662321099990647697175478273, 9304595970494411110326649421962412033, 167616699782206593882944206094565066958299591488831489

Offset: 1

N. J. A. Sloane, Dec 29 1999

nonn

Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

For more terms see A032353.

A002255 Numbers k such that 7*4^k + 1 is prime.

Original entry on oeis.org

1, 2, 3, 7, 10, 13, 25, 26, 46, 60, 87, 90, 95, 145, 160, 195, 216, 308, 415, 902, 1128, 3307, 6748, 7747, 8348, 11193, 27243, 44033, 47665, 103542, 141517, 280908, 402267, 405615, 745926, 1069956, 1083900, 1457977, 1507881, 1755887

Offset: 1

N. J. A. Sloane

H. Riesel, Prime numbers and computer methods for factorization, in 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.
C. K. Caldwell, The Prime Pages.
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
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.
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

See A032353 (which is the main entry for this sequence) for more terms.

is(n)=ispseudoprime(7*4^n+1) \\ Charles R Greathouse IV, Jun 06 2017

More terms (from A032353) added by Joerg Arndt, Apr 07 2013

A001771 Numbers k such that 7*2^k - 1 is prime.

Original entry on oeis.org

1, 5, 9, 17, 21, 29, 45, 177, 18381, 22529, 24557, 26109, 34857, 41957, 67421, 70209, 169085, 173489, 177977, 363929, 372897

Offset: 1

N. J. A. Sloane

k is always of the form 4*j + 1.

If k is in the sequence and m=2^(k+2)*3*(7*2^k-1) then phi(m)+sigma(m)=3m (m is in the sequence A011251). The proof is easy. - Farideh Firoozbakht, Mar 04 2005

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
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. A050523, A003307, A002235, A046865, A079906, A046866, A005541, A056725, A046867, A079907.

Cf. A032353 (7*2^k+1 is prime).

Do[ If[ PrimeQ[7*2^n - 1], Print[n]], {n, 1, 2500}]

v=[ ]; for(n=0,2000, if(isprime(7*2^n-1),v=concat(v,n),)); v

More terms from Douglas Burke (dburke(AT)nevada.edu).

More terms from Hugo Pfoertner, Jun 23 2004

A280003 Numbers k such that 7*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.

Original entry on oeis.org

14, 120, 290, 320, 95330, 2167800

Offset: 1

Arkadiusz Wesolowski, Feb 21 2017

18233956 belongs to this sequence, but its position is currently unknown. - Jeppe Stig Nielsen, Oct 05 2020

Proth Search Page, Prime factors of Fermat numbers
Eric Weisstein's World of Mathematics, Fermat Number

Subsequence of A032353.

Cf. A000215, A050527, A057778, A201364, A204620, A226366, A280004.

IsInteger := func; [n: n in [1..320] | IsPrime(k) and IsInteger(Log(2, Modorder(2, k))) where k is 7*2^n+1];

A269544 Numbers n such that 7*8^n + 1 is prime.

Original entry on oeis.org

2, 40, 58, 60, 130, 144, 752, 7462, 18162, 69028, 187272, 268178, 270410, 497284, 713304, 722600, 1005254

Offset: 1

Robert Price, Feb 29 2016

a(n) is even because 7*8^(2*k+1) + 1 is divisible by 3.

Cf. A056799, A245241, A268061.

Select[Range[0, 200000,2], PrimeQ[7*8^# + 1] &]

is(n)=ispseudoprime(7*8^n+1) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = A032353(n)/3 where this is an integer.

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

cp's OEIS Frontend

A050527 Primes of form 7*2^n+1.

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A002255 Numbers k such that 7*4^k + 1 is prime.

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A001771 Numbers k such that 7*2^k - 1 is prime.

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A280003 Numbers k such that 7*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.

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A269544 Numbers n such that 7*8^n + 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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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.