A274544 Values of k such that 2*k-1 and 5*k-1 are both perfect squares.

1, 13, 925, 18241, 1333345, 26303005, 1922682061, 37928914465, 2772506198113, 54693468355021, 3997952014996381, 78867943439025313, 5765044033118582785, 113727519745606145821, 8313189497804981379085, 163995004605220623248065, 11987613490790750030057281

Offset

1,2

Comments

Intersection of A001844 and A062317.

Links

Colin Barker, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

Formula

a(n) = a(n-1) + 1442*a(n-2) - 1442*a(n-3) - a(n-4) + a(n-5) for n>5.

G.f.: x*(1 + 12*x - 530*x^2 + 12*x^3 + x^4) / ((1 - x)*(1 - 38*x + x^2)*(1 + 38*x + x^2)).

Example

13 is in the sequence because 2*13-1 = 25 = 5^2, and 5*13-1 = 64 = 8^2.

Mathematica

Rest@ CoefficientList[Series[x (1 + 12 x - 530 x^2 + 12 x^3 + x^4)/((1 - x) (1 - 38 x + x^2) (1 + 38 x + x^2)), {x, 0, 17}], x] (* Michael De Vlieger, Jun 27 2016 *)

Prog

(PARI) Vec(x*(1+12*x-530*x^2+12*x^3+x^4)/((1-x)*(1-38*x+x^2)*(1+38*x+x^2))+ O(x^20))
(PARI) isok(n) = issquare(2*n-1) && issquare(5*n-1); \\ Michel Marcus, Jun 28 2016

Crossrefs

Cf. A001844, A062317, A274545.

Sequence in context: A196728 A197068 A337575 * A267915 A358983 A096084

Adjacent sequences: A274541 A274542 A274543 * A274545 A274546 A274547

Keyword

nonn,easy

Author

Colin Barker, Jun 27 2016

Status

approved