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Search: id:A129557
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| A129557 |
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Numbers k>0 such that k^2 is a centered pentagonal number. |
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+0
2
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| 1, 4, 34, 151, 1291, 5734, 49024, 217741, 1861621, 8268424, 70692574, 313982371, 2684456191, 11923061674, 101938642684, 452762361241, 3870983965801, 17193046665484, 146995452057754, 652883010927151, 5581956194228851
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Corresponding numbers n such that centered pentagonal number A005891(n) = (5n^2+5n+2)/2 is a perfect square are listed in A129556(n) = {0, 2, 21, 95, 816, 3626, 31005, ...}.
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics, Centered Pentagonal Number.
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FORMULA
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a(n) = Sqrt[ (5*A129556(n)^2 + 5*A129556(n) + 2)/2 ].
For n>=5, a(n) = 38*a(n-2) - a(n-4). [From Max Alekseyev (maxale(AT)gmail.com), May 08 2009]
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MATHEMATICA
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Do[ f=(5n^2+5n+2)/2; If[ IntegerQ[ Sqrt[f] ], Print[ Sqrt[f] ] ], {n, 1, 40000} ]
q=5; s=0; lst={}; Do[s+=n; If[Sqrt[q*s+1]==Floor[Sqrt[q*s+1]], AppendTo[lst, Sqrt[q*s+1]]], {n, 0, 8!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 02 2009]
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PROGRAM
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(PARI) A129557()={ for(n=1, 1000000000, f=(5*n^2+5*n+2)/2 ; if(issquare(f), print(round(sqrt(f))) ; ); ) ; } A129557() ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 11 2007
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CROSSREFS
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Cf. A005891 = Centered pentagonal numbers: (5n^2+5n+2)/2. Cf. A129556 = numbers n such that centered pentagonal number A005891(n) = (5n^2+5n+2)/2 is a perfect square.
Sequence in context: A053902 A054464 A002101 this_sequence A085695 A049293 A116430
Adjacent sequences: A129554 A129555 A129556 this_sequence A129558 A129559 A129560
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 20 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 11 2007
Formula and further terms from Max Alekseyev (maxale(AT)gmail.com), May 08 2009
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