

A062317


Numbers n such that 5*n1 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
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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+5n)^2 + 1)/5 if n is odd; a(n) = ((3+5n)^2 + 1)/5 if n is even.
From R. J. Mathar, Jan 30 2010: (Start)
a(n) = a(n1) + 2*a(n2)  2*a(n3)  a(n4) + a(n5).
G.f.: x*(1+x+6*x^2+x^3+x^4)/((1+x)^2*(1x)^3). (End)


MATHEMATICA

f[n_]:=IntegerQ[Sqrt[5*n1]]; 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*n1), 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



