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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(PARI) lista(n)={my(L=List(), k=0); while(#L<n, k++; my(t=k*(k+1)/4); if(!frac(t)&&isprime(t-1)&&isprime(t+1), listput(L, t-1))); Vec(L)} \\ Andrew Howroyd, Sep 18 2024

Crossrefs

Cf. A000217, A001359, A166119.

Sequence in context: A104165 A031391 A176783 * A243096 A221569 A179816

Adjacent sequences: A086813 A086814 A086815 * A086817 A086818 A086819

Keyword

nonn

Author

Jason Earls, Aug 06 2003

Extensions

Offset changed by Andrew Howroyd, Sep 18 2024

Status

approved