A101994 Numbers k such that 4*k-1, 8*k-1, 16*k-1, 32*k-1 and 64*k-1 are all primes.

45, 13410, 15855, 31710, 31785, 63570, 74025, 85230, 151830, 202635, 267300, 280665, 399675, 405405, 455250, 466560, 478170, 480240, 511335, 534600, 539475, 561330, 569520, 589305, 666945, 716460, 743160, 748215, 766785, 799350, 860835

Offset: 1

Author

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

Keywords

• easy
• nonn

Examples

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

Links

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

Crossrefs

Cf. A002515, A101995, A101996, A101997, A101998, A101999.

Subsequence of A005099, A005122, A101790 and A101794.

Programs

Mathematica

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

PARI

is(k) = isprime(4*k-1) && isprime(8*k-1) && isprime(16*k-1) && isprime(32*k-1) && isprime(64*k-1); \\ Amiram Eldar, May 13 2024