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

Author

Santi Spadaro, Jul 12 2001

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A036666.

Programs

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 *)

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

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

Extensions

More terms from Jason Earls, Jul 14 2001