A101791 Primes of the form 4*k-1 such that 8*k-1 and 16*k-1 are also primes.

11, 179, 359, 719, 1019, 1031, 1451, 1511, 1811, 1931, 2459, 2699, 2819, 3491, 3539, 3911, 5399, 6131, 7079, 7151, 10691, 11171, 11471, 12119, 12899, 12959, 16811, 17159, 18191, 19319, 19991, 20411, 21011, 21179, 22271, 23099, 23819

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) = 4*A101790(n) - 1. - Amiram Eldar, May 13 2024

Example

4*3-1 = 11, 8*3-1 = 23 and 16*3-1 = 47 are primes, so 11 is a term.

Mathematica

p4816Q[n_]:=Module[{nn=(n+1)/4}, And@@PrimeQ[{n, 8nn-1, 16nn-1}]]; Select[ 4*Range[6000]-1, p4816Q] (* Harvey P. Dale, Nov 25 2011 *)

Prog

(PARI) is(k) = if(k % 4 == 3, my(m = k\4 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1), 0); \\ Amiram Eldar, May 13 2024

Crossrefs

Cf. A002515, A101790, A101792, A101793.

Subsequence of A002145.

Subsequences: A101795, A101995.

Sequence in context: A081740 A051687 A231916 * A140034 A363024 A162715

Adjacent sequences: A101788 A101789 A101790 * A101792 A101793 A101794

Keyword

easy,nonn

Author

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

Status

approved