This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218273 #18 Oct 17 2013 21:33:26 %S A218273 1225,1413721,48024900,1631432881,1882672131025,63955431761796, %T A218273 2172602007770041,73804512832419600,85170343853180456676, %U A218273 2893284510173841030625,98286503002057414584576,3338847817559778254844961,113422539294030403250144100 %N A218273 Square triangular numbers that can be expressed as sums of a positive square number and a positive triangular number. Intersection of A182427 and A214937. %C A218273 Theorem (I. N. Ianakiev): There are infinitely many such numbers. Proof: Any A001110(2n+1), for n>0, is such a number as A001110(2n+1) = (2a+1)^2+(4a^2+4a)(4a^2+4a+1)(1/2), where a = (A002315(n)-1)(1/2). Note: other numbers, not of the form A001110(2n+1), e.g. A001110(6), are also in the sequence (see the example below). %C A218273 Every term is divisible by its digital root (A010888). - _Ivan N. Ianakiev_, Oct 17 2013 %e A218273 a(3) = A001110(6) = 48024900 = 6918^2 + [576*577*(1/2)]. %Y A218273 Cf. A000217, A000290, A001110, A182427, A214937. %K A218273 nonn,more %O A218273 1,1 %A A218273 _Ivan N. Ianakiev_, Oct 25 2012 %E A218273 a(8)-a(13) from _Donovan Johnson_, Nov 02 2012