A101998 Primes of the form 32*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 64*k-1 are also primes.

1439, 429119, 507359, 1014719, 1017119, 2034239, 2368799, 2727359, 4858559, 6484319, 8553599, 8981279, 12789599, 12972959, 14567999, 14929919, 15301439, 15367679, 16362719, 17107199, 17263199, 17962559, 18224639, 18857759

Offset

1,1

Links

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

Formula

a(n) = 32*A101994(n) - 1 = 8*A101995(n) + 7 = 4*A101996(n) + 3 = 2*A101997(n) + 1. - Amiram Eldar, May 13 2024

Example

4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 1439 is a term.

Mathematica

32 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 6]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)

Prog

(PARI) is(k) = if(k % 32 == 31, my(m = k\32 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1) && isprime(64*m-1), 0); \\ Amiram Eldar, May 13 2024

Crossrefs

Cf. A101994, A101995, A101996, A101997, A101999.

Subsequence of A127578 and A101798.

Sequence in context: A351677 A101798 A081426 * A174277 A063846 A252186

Adjacent sequences: A101995 A101996 A101997 * A101999 A102000 A102001

Keyword

easy,nonn

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004

Status

approved