A053611 - OEIS

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A053611

Numbers n such that 1 + 4 + 9 + ... + n^2 = 1 + 2 + 3 + ... + s for some s.

1, 5, 6, 85 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`These are the only possibilities for a sum of the first n squares to equal a triangular number.`
	REFERENCES	`E. T. Avanesov, The Diophantine equation 3y(y+1) = x(x+1)(2x+1), Volz. Mat. Sb. Vyp., 8 (1971), 3-6.` `R. Finkelstein and H. London, On triangular numbers which are sums of consecutive squares, J. Number Theory, 4 (1972), 455-462.` `Joe Roberts, Lure of the Integers, page 245 (entry for 645).`
	EXAMPLE	`1^2+2^2+3^2+4^2+5^2 = 1+2+3+...+10, so 5 is in the sequence.`
	MAPLE	`istriangular:=proc(n) local t1; t1:=floor(sqrt(2n)); if n = t1(t1+1)/2 then RETURN(true) else RETURN(false); fi; end;` `M:=1000; for n from 1 to M do if istriangular(n(n+1)(2n+1)/6) then lprint(n, n(n+1)(2n+1)/6); fi; od: (Maple program from N. J. A. Sloane (njas(AT)research.att.com))`
	CROSSREFS	`Cf. A039596 (values of s), A053612.` `Sequence in context: A111504 A041057 A041058 * A041139 A065354 A078984` `Adjacent sequences: A053608 A053609 A053610 * A053612 A053613 A053614`
	KEYWORD	`fini,full,nonn,bref`
	AUTHOR	`Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Mar 19 2000`
	EXTENSIONS	`Edited by N. J. A. Sloane (njas(AT)research.att.com), May 25 2008`

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Last modified February 16 21:04 EST 2012. Contains 205969 sequences.