Search: id:A036666
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%I A036666
%S A036666 0,3,7,16,24,39,51,72,88,115,135,168,192,231,259,304,336,387,423,
%T A036666 480,520,583,627,696,744,819,871,952,1008,1095,1155,1248,1312,1411,
%U A036666 1479,1584,1656,1767,1843,1960,2040,2163,2247,2376,2464,2599,2691
%N A036666 Numbers n such that 5n+1 is a perfect square.
%C A036666 Third differences are 4, -6, 8, -10, 12, -14, 16, -18, 20, -22, 24, -26, 
               28,...
%C A036666 Sequence allows us to find X values of the equation: 5*X^3 + X^2 = Y^2. 
               - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
%H A036666 R. Stephan, <a href="http://www.ark.in-berlin.de/A001082.ps">On the solutions 
               to 'px+1 is square'</a>
%F A036666 Expansion of x*(3+4*x+3*x^2)/((1-x)*(1-x^2)).
%F A036666 a(n) = ((5k+1)^2-1)/5 if n is odd; a(n) = ((5k+4)^2-1)/5 if n is even.
%F A036666 a(2n)=n(5n+2), a(2n+1)=5*n^2+8n+3. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), 
               Nov 06 2007
%F A036666 Also, for all a(n) even, is a(n)=[4n*(n+1)]/5; example: n=4, a(4)=16; 
               n=5, a(5)=24; n=9, a(9)=72; n=10, a(10)=88. [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Jan 24 2009]
%t A036666 (Select[ Range[121], Mod[ #, 5] == 1 || Mod[ #, 5] == 4 &]^2 - 1)/5 (from 
               Robert G. Wilson v Jun 23 2004)
%Y A036666 Cf. A005563, A046092, A001082, A002378.
%Y A036666 Sequence in context: A162159 A004782 A116040 this_sequence A117491 A110585 
               A000412
%Y A036666 Adjacent sequences: A036663 A036664 A036665 this_sequence A036667 A036668 
               A036669
%K A036666 nonn
%O A036666 1,2
%A A036666 N. J. A. Sloane (njas(AT)research.att.com).
%E A036666 Better description and additional formula from Santi Spadaro (spados(AT)katamail.com), 
               Jul 12 2001

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