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 A129445 Numbers k>0 such that k^2 is a centered triangular number. 5
 1, 2, 8, 19, 79, 188, 782, 1861, 7741, 18422, 76628, 182359, 758539, 1805168, 7508762, 17869321, 74329081, 176888042, 735782048, 1751011099, 7283491399, 17333222948, 72099131942, 171581218381, 713707828021, 1698478960862 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Corresponding numbers n such that centered triangular number A005448(n) is a perfect square are listed in A129444(n). LINKS _Alexander Adamchuk_, Apr 26 2007, Table of n, a(n) for n = 1..100 Tom Beldon and Tony Gardiner, Triangular Numbers and Perfect Squares, The Mathematical Gazette, Vol. 86, No. 507, (2002), pp. 423-431. [Ant King, Dec 07 2010] FORMULA a(n) = Sqrt[ 3*A129444(n)*(A129444(n) - 1)/2 + 1 ]. Empirical G.f.: x*(1-x)*(1+3*x+x^2)/(1-10*x^2+x^4). [Colin Barker, Apr 11 2012] MATHEMATICA Do[ f = 3n(n-1)/2 + 1; If[ IntegerQ[ Sqrt[f] ], Print[ Sqrt[f] ] ], {n, 1, 150000} ] CROSSREFS Cf. A005448, A129444. Prime terms are listed in A129446. Sequence in context: A026588 A026572 A074797 * A082821 A188893 A030097 Adjacent sequences:  A129442 A129443 A129444 * A129446 A129447 A129448 KEYWORD nonn AUTHOR Alexander Adamchuk, Apr 15 2007, Apr 26 2007 EXTENSIONS More terms from Alexander Adamchuk, Apr 26 2007 STATUS approved

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Last modified May 21 15:07 EDT 2013. Contains 225504 sequences.