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%I #18 Oct 17 2013 21:33:26
%S 1225,1413721,48024900,1631432881,1882672131025,63955431761796,
%T 2172602007770041,73804512832419600,85170343853180456676,
%U 2893284510173841030625,98286503002057414584576,3338847817559778254844961,113422539294030403250144100
%N 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 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 Every term is divisible by its digital root (A010888). - _Ivan N. Ianakiev_, Oct 17 2013
%e a(3) = A001110(6) = 48024900 = 6918^2 + [576*577*(1/2)].
%Y Cf. A000217, A000290, A001110, A182427, A214937.
%K nonn,more
%O 1,1
%A _Ivan N. Ianakiev_, Oct 25 2012
%E a(8)-a(13) from _Donovan Johnson_, Nov 02 2012