A024899 Numbers k such that 6*k + 1 is prime.

1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 21, 23, 25, 26, 27, 30, 32, 33, 35, 37, 38, 40, 45, 46, 47, 51, 52, 55, 56, 58, 61, 62, 63, 66, 68, 70, 72, 73, 76, 77, 81, 83, 87, 90, 91, 95, 96, 100, 101, 102, 103, 105, 107, 110, 112, 115, 118, 121, 122, 123, 125, 126, 128, 131, 135, 137

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

For all elements of this sequence there are no (x,y) positive integers such that a(n)=6*x*y+x+y or a(n)=6*x*y-x-y. - Pedro Caceres, Apr 19 2019

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

A002476 gives primes, A091178 gives prime index.

Complement of A046954 relative to A000027.

Programs

Magma

[n: n in [0..200]| IsPrime(6*n+1)] // Vincenzo Librandi, Nov 20 2010

Maple

a := [ ]: for n from 0 to 400 do if isprime(6*n+1) then a := [ op(a), n ]; fi; od: A002476 := n->a[n];

Mathematica

Select[Range@ 140, PrimeQ[6 # + 1] &] (* Michael De Vlieger, Jan 23 2018 *)

PARI

select(n->n%6==1,primes(100))\6 \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = A024892(n)/2 = (A034936(n)+1)/2. - Ray Chandler, Dec 26 2003

a(n) = (A002476(n)-1)/6. - Zak Seidov, Aug 31 2016