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Search: id:A053755
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| 1, 5, 17, 37, 65, 101, 145, 197, 257, 325, 401, 485, 577, 677, 785, 901, 1025, 1157, 1297, 1445, 1601, 1765, 1937, 2117, 2305, 2501, 2705, 2917, 3137, 3365, 3601, 3845, 4097, 4357, 4625, 4901, 5185, 5477, 5777, 6085, 6401, 6725, 7057
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also numbers of the form 4k+1 whose prime factors are all of the form 4k+1. E.g. 40001 = 13*17*181, 13=3*4+1,17=4*4+1,181=4*45+1. - Cino Hilliard (hillcino368(AT)gmail.com), Aug 26 2006
A000466(n), A008586(n) and A053755(n) are Pythagorean triples. - Zak Seidov, Jan 16 2007
a(n) = A156701(n)/A087475(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 13 2009]
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 3.
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FORMULA
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a(n)=A000466(n)+2. - Zak Seidov, Jan 16 2007
O.g.f.: -(1+2*x+5*x^2)/(-1+x)^3. a(n) = 3a(n-1)-3a(n-2)+a(n-3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2008
Equals binomial transform of [1, 4, 8, 0, 0, 0,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 30 2008
a(n)=8*n+a(n-1)-12 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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EXAMPLE
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For n=2, a(2)=8*2+1-12=5; n=3, a(3)=8*3+5-12=17; n=4, a(4)=8*4+17-12=37 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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MAPLE
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with (combinat):seq(fibonacci(3, 2*n), n=0..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 21 2008
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MATHEMATICA
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lst={}; Do[p=4*n^2+1; AppendTo[lst, p], {n, 1, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 02 2008]
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PROGRAM
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(PARI) for(x=0, 100, print1(4*x^2+1", ")) - Cino Hilliard (hillcino368(AT)gmail.com), Aug 26 2006
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CROSSREFS
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Sequence in context: A080167 A060245 A119456 this_sequence A162373 A146781 A107199
Adjacent sequences: A053752 A053753 A053754 this_sequence A053756 A053757 A053758
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KEYWORD
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nonn,easy,new
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AUTHOR
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Stuart M. Ellerstein (ellerstein(AT)aol.com), Apr 06 2000
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