A101997 Primes of the form 16*k-1 such that 4*k-1, 8*k-1, 32*k-1 and 64*k-1 are also primes.

719, 214559, 253679, 507359, 508559, 1017119, 1184399, 1363679, 2429279, 3242159, 4276799, 4490639, 6394799, 6486479, 7283999, 7464959, 7650719, 7683839, 8181359, 8553599, 8631599, 8981279, 9112319, 9428879, 10671119

Offset

1,1

Links

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

Formula

a(n) = 16*A101994(n) - 1 = 4*A101995(n) + 3 = 2*A101996(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 719 is a term.

Mathematica

Select[With[{c=2^Range[2, 6]}, Table[c n-1, {n, 700000}]], AllTrue[#, PrimeQ]&][[All, 3]] (* Harvey P. Dale, Nov 29 2018 *)

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) && isprime(64*m-1), 0); \\ Amiram Eldar, May 13 2024

Crossrefs

Cf. A101994, A101995, A101996, A101998, A101999.

Subsequence of A127576, A101793 and A101797.

Sequence in context: A139177 A064980 A290120 * A139195 A269124 A267336

Adjacent sequences: A101994 A101995 A101996 * A101998 A101999 A102000

Keyword

easy,nonn

Author

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

Status

approved