A086816 Smaller member of a twin prime pair with a triangular sum.

17, 59, 137, 149, 1277, 1619, 2729, 4127, 6359, 11717, 13397, 17489, 20807, 23027, 28307, 29669, 51869, 61379, 69827, 73847, 78539, 92567, 97499, 115769, 138569, 166667, 176609, 193379, 200927, 258317, 304979, 430007, 500909, 518759, 536189

Offset: 1

Author

Jason Earls, Aug 06 2003

Keywords

• nonn

Comments

It is easily shown that all terms end in 7 or 9.

Examples

			59 is a term because it is the smaller member of the twin prime pair (59,61) and 59 + 61 = 120 = 15*(15+1)/2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000217, A001359, A166119.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[45000]],2,1],#[[2]]-#[[1]]==2 && IntegerQ[(Sqrt[1+8Total[#]]-1)/2]&]][[1]] (* Harvey P. Dale, Dec 15 2011 *)

PARI

lista(n)={my(L=List(), k=0); while(#LAndrew Howroyd, Sep 18 2024

Formula

a(n) = 6*A166119(n) - 1. - Hugo Pfoertner, Sep 18 2024

Extensions

Offset changed by Andrew Howroyd, Sep 18 2024