A274545 Values of k such that 5*k-1 and 10*k-1 are both perfect squares.

1, 29, 33293, 1130977, 1305146305, 44336554445, 51164345409437, 1738081606216033, 2005744667435597089, 68136275082544365341, 78629202401645931667661, 2671078254047822603875969, 3082421990543579145800043553, 104711609647046466634601365517

Offset: 1

Author

Colin Barker, Jun 27 2016

Keywords

• nonn
• easy

Comments

Intersection of A062317 and A220082.

Examples

			29 is in the sequence because 5*29-1 = 144 = 12^2, and 10*29-1 = 289 = 17^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..400
• Index entries for linear recurrences with constant coefficients, signature (1,39202,-39202,-1,1).

Crossrefs

Cf. A062317, A220082, A274544.

Programs

Mathematica

Rest@ CoefficientList[Series[x (1 + 28 x- 5938 x^2 + 28 x^3 + x^4) / ((1 - x) (1 - 198 x + x^2) (1 + 198 x + x^2)), {x, 0, 17}], x] (* Michael De Vlieger, Jun 27 2016 *)

PARI

Vec(x*(1+x)*(1-6*x+x^2)/((1-x)*(1-34*x+x^2)*(1+x+x^2)) + O(x^20))

PARI

isok(n) = issquare(5*n-1) && issquare(10*n-1); \\ Michel Marcus, Jun 28 2016

Formula

a(n) = a(n-1) + 39202*a(n-2) - 39202*a(n-3) - a(n-4) + a(n-5) for n>5.

G.f.: x*(1 + 28*x - 5938*x^2 + 28*x^3 + x^4)/((1 - x)*(1 - 198*x + x^2)*(1 + 198*x + x^2)).