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

1,1

Links

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

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

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 2879 is a term.

Mathematica

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

Prog

(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

Crossrefs

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

Subsequence of A127579.

Sequence in context: A261859 A286526 A081427 * A066174 A175750 A179703

Adjacent sequences: A101996 A101997 A101998 * A102000 A102001 A102002

Keyword

easy,nonn

Author

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

Status

approved