A101797 Primes of the form 16*k-1 such that 4*k-1, 8*k-1 and 32*k-1 are also primes.

719, 1439, 10799, 14159, 48479, 68639, 109919, 214559, 231359, 253679, 285599, 298799, 329999, 350159, 405599, 429119, 430799, 451679, 488399, 491279, 507359, 508559, 533999, 557759, 666959, 671039, 918959, 1014719, 1017119, 1148879

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

a(n) = 16*A101794(n) - 1 = 4*A101795(n) + 3 = 2*A101796(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 719 is a term.

Mathematica

16#-1&/@Select[Range[80000], AllTrue[#*2^Range[2, 5]-1, PrimeQ]&] (* Harvey P. Dale, Apr 25 2015 *)

Prog

(PARI) is(k) = if(k % 16 == 15, my(m = k\16 + 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, A101798.

Subsequence of A127576 and A101793.

Subsequence: A101997.

Sequence in context: A351669 A361345 A081425 * A144767 A127227 A139177

Adjacent sequences: A101794 A101795 A101796 * A101798 A101799 A101800

Keyword

easy,nonn

Author

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

Status

approved