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A145856 Least number k>1 such that centered n-gonal number n*k(k-1)/2+1 is a perfect square, or 0 if there no such k exists. 0

%I #8 Mar 31 2012 13:20:40

%S 3,0,2,4,3,8,16,2,17,9,15,5,6,16,2,3,6,0,7,4,3,40,7,2,22,8,111,4,16,8,

%T 16,0,3,9,2,5,990,9,15,3,46,16,10,5,6,336,10,2,30,0,31,16,11,416,7,3,

%U 11,33,55,4,78,56,2,6,3,8,47751,12,16,24,48,0,49,25,17,13,6,9,2640,2,6721

%N Least number k>1 such that centered n-gonal number n*k(k-1)/2+1 is a perfect square, or 0 if there no such k exists.

%D Jonathan Vos Post, When Centered Polygonal Numbers are Perfect Squares, submitted to Mathematics Magazine, 4 May 2004, manuscript no. 04-1165, unpublished, available upon request [From _Jonathan Vos Post_, Oct 25 2008]

%H E. Weisstein, MathWorld, <a href="http://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Numbers</a>

%H <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>

%F a(n) = 0 for n in A166259.

%F a(n) = A120744(n) + 1. [From _Alexander Adamchuk_, Oct 10 2009]

%Y Cf. A120744, A001542, A166259, A006451, A001921, A129444, A001570, A001652, A129556, A053606, A105038, A105040, A053141, A061278.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Oct 22 2008

%E Edited by _Max Alekseyev_, Jan 20 2010

%E Edited by _Max Alekseyev_, Jan 23 2010

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)