A062317 Numbers k such that 5*k-1 is a perfect square.

1, 2, 10, 13, 29, 34, 58, 65, 97, 106, 146, 157, 205, 218, 274, 289, 353, 370, 442, 461, 541, 562, 650, 673, 769, 794, 898, 925, 1037, 1066, 1186, 1217, 1345, 1378, 1514, 1549, 1693, 1730, 1882, 1921, 2081, 2122, 2290, 2333, 2509, 2554, 2738, 2785, 2977

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

a(n) = ((2+5*(n-1)/2)^2 + 1)/5 if n is odd; a(n) = ((3+5*(n-2)/2)^2 + 1)/5 if n is even.

From R. J. Mathar, Jan 30 2010: (Start)

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

G.f.: x*(1+x+6*x^2+x^3+x^4)/((1+x)^2*(1-x)^3). (End)

a(n) = (10*n*(n-1) + 5 - (6*n-3)*(-1)^n)/8. - Eric Simon Jacob, Jan 20 2020

Mathematica

f[n_]:=IntegerQ[Sqrt[5*n-1]]; Select[Range[0, 8! ], f[ # ]&] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 2, 10, 13, 29}, 50] (* Harvey P. Dale, Dec 29 2018 *)

Prog

(PARI) je=[]; for(n=1, 5000, if(issquare(5*n-1), je=concat(je, n))); je
(PARI) { n=0; for (m=1, 10^9, if (issquare(5*m - 1), write("b062317.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 04 2009

Crossrefs

Cf. A036666.

Sequence in context: A297998 A037386 A250187 * A140510 A277087 A098735

Adjacent sequences: A062314 A062315 A062316 * A062318 A062319 A062320

Keyword

nonn,easy

Author

Santi Spadaro, Jul 12 2001

Extensions

More terms from Jason Earls, Jul 14 2001

Status

approved