A101798 Primes of the form 32*k-1 such that 4*k-1, 8*k-1 and 16*k-1 are also primes.

1439, 2879, 21599, 28319, 96959, 137279, 219839, 429119, 462719, 507359, 571199, 597599, 659999, 700319, 811199, 858239, 861599, 903359, 976799, 982559, 1014719, 1017119, 1067999, 1115519, 1333919, 1342079, 1837919, 2029439, 2034239

Offset

1,1

Links

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

Formula

a(n) = 32*A101794(n) - 1 = 8*A101795(n) + 7 = 4*A101796(n) + 3 = 2*A101797(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 1439 is a term.

Mathematica

32 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 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), 0); \\ Amiram Eldar, May 13 2024

Crossrefs

Cf. A002515, A101794, A101795, A101796, A101797.

Subsequence of A127578.

Subsequence: A101998.

Sequence in context: A227494 A352249 A351677 * A081426 A101998 A174277

Adjacent sequences: A101795 A101796 A101797 * A101799 A101800 A101801

Keyword

easy,nonn

Author

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

Status

approved