A101999 Primes of the form 64*k-1 such that 4*k-1, 8*k-1, 16*k-1 and 32*k-1 are also primes.

2879, 858239, 1014719, 2029439, 2034239, 4068479, 4737599, 5454719, 9717119, 12968639, 17107199, 17962559, 25579199, 25945919, 29135999, 29859839, 30602879, 30735359, 32725439, 34214399, 34526399, 35925119, 36449279

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 2879 is a term.
		

Links

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

Crossrefs

Cf. A101994, A101995, A101996, A101997, A101998.

Subsequence of A127579.

Programs

Mathematica

64#-1&/@Select[Range[570000],AllTrue[#*2^Range[2,6]-1,PrimeQ]&] (* Harvey P. Dale, Aug 07 2021 *)

PARI

is(k) = if(k % 64 == 63, my(m = k\64 + 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

Formula

a(n) = 64*A101994(n) - 1 = 16*A101995(n) + 15 = 8*A101996(n) + 7 = 4*A101997(n) + 3 = 2*A101998(n) + 1. - Amiram Eldar, May 13 2024