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Search: id:A036666
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| A036666 |
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Numbers n such that 5n+1 is a perfect square. |
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+0
13
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| 0, 3, 7, 16, 24, 39, 51, 72, 88, 115, 135, 168, 192, 231, 259, 304, 336, 387, 423, 480, 520, 583, 627, 696, 744, 819, 871, 952, 1008, 1095, 1155, 1248, 1312, 1411, 1479, 1584, 1656, 1767, 1843, 1960, 2040, 2163, 2247, 2376, 2464, 2599, 2691
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Third differences are 4, -6, 8, -10, 12, -14, 16, -18, 20, -22, 24, -26, 28,...
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
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LINKS
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R. Stephan, On the solutions to 'px+1 is square'
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FORMULA
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Expansion of x*(3+4*x+3*x^2)/((1-x)*(1-x^2)).
a(n) = ((5k+1)^2-1)/5 if n is odd; a(n) = ((5k+4)^2-1)/5 if n is even.
a(2n)=n(5n+2), a(2n+1)=5*n^2+8n+3. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 06 2007
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]
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MATHEMATICA
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(Select[ Range[121], Mod[ #, 5] == 1 || Mod[ #, 5] == 4 &]^2 - 1)/5 (from Robert G. Wilson v Jun 23 2004)
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CROSSREFS
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Cf. A005563, A046092, A001082, A002378.
Sequence in context: A162159 A004782 A116040 this_sequence A117491 A110585 A000412
Adjacent sequences: A036663 A036664 A036665 this_sequence A036667 A036668 A036669
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description and additional formula from Santi Spadaro (spados(AT)katamail.com), Jul 12 2001
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