A101996 Primes of the form 8*k-1 such that 4*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.

359, 107279, 126839, 253679, 254279, 508559, 592199, 681839, 1214639, 1621079, 2138399, 2245319, 3197399, 3243239, 3641999, 3732479, 3825359, 3841919, 4090679, 4276799, 4315799, 4490639, 4556159, 4714439, 5335559, 5731679

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..750 from Harvey P. Dale)

Formula

a(n) = 8*A101994(n) - 1 = 2*A101995(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 359 is a term.

Mathematica

8#-1&/@Select[Range[720000], AllTrue[{4, 8, 16, 32, 64}#-1, PrimeQ]&] (* Harvey P. Dale, Jan 17 2023 *)
Select[Table[2^Range[2, 6] n-1, {n, 750000}], AllTrue[#, PrimeQ]&][[;; , 2]] (* Harvey P. Dale, Jun 03 2023 *)

Prog

(PARI) is(k) = if(k % 8 == 7, my(m = k\8 + 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. A101789, A101994, A101995, A101997, A101998, A101999.

Subsequence of A007522, A101792 and A101796.

Sequence in context: A013325 A344284 A179678 * A237017 A360943 A097570

Adjacent sequences: A101993 A101994 A101995 * A101997 A101998 A101999

Keyword

easy,nonn

Author

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

Extensions

Corrected by T. D. Noe, Nov 15 2006

Status

approved