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

Author

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

Keywords

• easy
• nonn

Examples

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

Links

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

Crossrefs

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

Subsequence of A007522 and A101792.

Subsequence: A101996.

Programs

Mathematica

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

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

Formula

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