cp's OEIS Frontend

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

%I A145856 #17 Jun 17 2025 11:54:32
%S A145856 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 A145856 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 A145856 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 A145856 Least number k>1 such that centered n-gonal number n*k(k-1)/2+1 is a perfect square, or 0 if no such k exists.
%D A145856 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Centered Polygonal Numbers are Perfect Squares, submitted to Mathematics Magazine, 4 May 2004, manuscript no. 04-1165, unpublished, available upon request. - _Jonathan Vos Post_, Oct 25 2008
%H A145856 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Numbers</a>
%H A145856 <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%F A145856 a(n) = 0 for n in A166259.
%F A145856 a(n) = A120744(n) + 1. -  _Alexander Adamchuk_, Oct 10 2009
%Y A145856 Cf. A120744, A001542, A166259, A006451, A001921, A129444, A001570, A001652, A129556, A053606, A105038, A105040, A053141, A061278.
%K A145856 nonn
%O A145856 1,1
%A A145856 _Alexander Adamchuk_, Oct 22 2008
%E A145856 Edited by _Max Alekseyev_, Jan 23 2010