A101796 Primes of the form 8*k-1 such that 4*k-1, 16*k-1 and 32*k-1 are also primes.

359, 719, 5399, 7079, 24239, 34319, 54959, 107279, 115679, 126839, 142799, 149399, 164999, 175079, 202799, 214559, 215399, 225839, 244199, 245639, 253679, 254279, 266999, 278879, 333479, 335519, 459479, 507359, 508559

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = 8*A101794(n) - 1 = 2*A101795(n) + 1. - Amiram Eldar, May 13 2024

Example

4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719 and 32*45-1 = 1439 are primes, so 359 is a term.

Mathematica

8 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)

Prog

(PARI) is(k) = if(k % 8 == 7, my(m = k\8 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ Amiram Eldar, May 13 2024

Crossrefs

Cf. A002515, A101794, A101795, A101797, A101798.

Subsequence of A007522 and A101792.

Subsequence: A101996.

Sequence in context: A344286 A142381 A054826 * A175537 A142852 A158307

Adjacent sequences: A101793 A101794 A101795 * A101797 A101798 A101799

Keyword

easy,nonn

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Status

approved