A274588 Values of n such that 2*n-1 and 7*n-1 are both triangular numbers.

1, 8, 638, 6931, 572671, 6223778, 514257668, 5588945461, 461802812941, 5018866799948, 414698411763098, 4506936797407591, 372398711960448811, 4047224225205216518, 334413628642071268928, 3634402847297487025321, 300303066121868039048281

Offset: 1

Author

Colin Barker, Jun 29 2016

Keywords

• nonn
• easy

Examples

			8 is in the sequence because 2*8-1 = 15, 7*8-1 = 55, and 15 and 55 are both triangular numbers.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..650
• Index entries for linear recurrences with constant coefficients, signature (1,898,-898,-1,1).

Crossrefs

Cf. A069099, A174114, A274587.

Programs

Mathematica

CoefficientList[Series[(1 + 7 x - 268 x^2 + 7 x^3 + x^4)/((1 - x) (1 - 30 x + x^2) (1 + 30 x + x^2)), {x, 0, 16}], x] (* Michael De Vlieger, Jun 30 2016 *)
LinearRecurrence[{1,898,-898,-1,1},{1,8,638,6931,572671},20] (* Harvey P. Dale, Apr 10 2023 *)

PARI

isok(n) = ispolygonal(2*n-1, 3) && ispolygonal(7*n-1, 3)

PARI

Vec((1+7*x-268*x^2+7*x^3+x^4)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20))

Formula

Intersection of A069099 and A174114.

G.f.: (1+7*x-268*x^2+7*x^3+x^4) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).