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A062317 Numbers k such that 5*k-1 is a perfect square. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 19:30 EDT 2021. Contains 347534 sequences. (Running on oeis4.)