A116602 Values n such that prime(2*n) mod 12 == 5.

5, 8, 12, 13, 15, 20, 30, 31, 33, 49, 51, 52, 54, 58, 63, 70, 71, 74, 76, 79, 80, 81, 85, 88, 89, 92, 93, 97, 98, 103, 106, 109, 110, 117, 119, 126, 134, 135, 144, 145, 148, 149, 151, 156, 160, 165, 166, 169, 171, 175, 178, 181, 191, 192, 196, 199, 200, 201, 202, 204

Offset: 1

Author

Roger L. Bagula, Mar 29 2006

Keywords

• nonn
• easy

Comments

Eight sets of integers (this, A116610 and A116612-A116617), dealing with the remainder classes {1,5,7,11} modulo 12 are inspired by the Taylor series of sin(x) = x-x^3/3!+x^5/5!-... and cos(x)=1-x^2/2!+x^4/4!-x^6/6!+... which might be constructed via partitioning of the series terms according to factorial denominators of 2n+1 = 1,3,5,7,.. and 2n=1,2,4,6,...

Examples

			33 is in the sequence because the 66th prime is 317 and 317 mod 12=5.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Programs

Maple

a:=proc(n) if ithprime(2*n) mod 12 = 5 then n fi end: seq(a(n),n=1..220);

Mathematica

a[1] = Flatten[Table[If[Mod[Prime[2*n], 12] == 5, n, {}], {n, 1, 100}]]
Select[Range[210],Mod[Prime[2#],12]==5&] (* Harvey P. Dale, Apr 12 2018 *)

PARI

for(n=1,999, prime(2*n)%12==5 & print1(n",")) \\ M. F. Hasler, May 22 2009

Formula

A116602 = 1/2 * {even terms in A160591}. - M. F. Hasler, May 22 2009

Extensions

Edited by N. J. A. Sloane, Apr 05 2006, May 22 2009