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

1,2

Comments

Intersection of A062317 and A220082.

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).

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)).

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A062317, A220082, A274544.

Sequence in context: A127425 A135253 A262715 * A296176 A159437 A343451

Adjacent sequences: A274542 A274543 A274544 * A274546 A274547 A274548

Keyword

nonn,easy

Author

Colin Barker, Jun 27 2016

Status

approved