A101995 Primes of the form 4*k-1 such that 8*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.

179, 53639, 63419, 126839, 127139, 254279, 296099, 340919, 607319, 810539, 1069199, 1122659, 1598699, 1621619, 1820999, 1866239, 1912679, 1920959, 2045339, 2138399, 2157899, 2245319, 2278079, 2357219, 2667779, 2865839

Offset

1,1

Links

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

Formula

a(n) = 4*A101994(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 179 is a term.

Mathematica

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

Prog

(PARI) is(k) = if(k % 4 == 3, my(m = k\4 + 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. A002515, A101794.

Cf. A101994, A101996, A101997, A101998, A101999.

Subsequence of A002145, A101791 and A101795.

Sequence in context: A168537 A130736 A200955 * A293141 A036203 A053325

Adjacent sequences: A101992 A101993 A101994 * A101996 A101997 A101998

Keyword

easy,nonn

Author

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

Status

approved