%I A053611
%S A053611 1,5,6,85
%N A053611 Numbers n such that 1 + 4 + 9 + ... + n^2 = 1 + 2 + 3 + ... + s for some 
               s.
%C A053611 These are the only possibilities for a sum of the first n squares to 
               equal a triangular number.
%D A053611 E. T. Avanesov, The Diophantine equation 3y(y+1) = x(x+1)(2x+1), Volz. 
               Mat. Sb. Vyp., 8 (1971), 3-6.
%D A053611 R. Finkelstein and H. London, On triangular numbers which are sums of 
               consecutive squares, J. Number Theory, 4 (1972), 455-462.
%D A053611 Joe Roberts, Lure of the Integers, page 245 (entry for 645).
%e A053611 1^2+2^2+3^2+4^2+5^2 = 1+2+3+...+10, so 5 is in the sequence.
%p A053611 istriangular:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/
               2 then RETURN(true) else RETURN(false); fi; end;
%p A053611 M:=1000; for n from 1 to M do if istriangular(n*(n+1)*(2*n+1)/6) then 
               lprint(n,n*(n+1)*(2*n+1)/6); fi; od: (Maple program from N. J. A. 
               Sloane (njas(AT)research.att.com))
%Y A053611 Cf. A039596 (values of s), A053612.
%Y A053611 Sequence in context: A111504 A041057 A041058 this_sequence A041139 A065354 
               A078984
%Y A053611 Adjacent sequences: A053608 A053609 A053610 this_sequence A053612 A053613 
               A053614
%K A053611 fini,full,nonn,bref
%O A053611 1,2
%A A053611 Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000
%E A053611 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 25 2008