[seqfan] Re: A006451 = n such that n*(n+1)/2+1 is square?

Richard Mathar mathar at strw.leidenuniv.nl
Sat Oct 10 14:34:47 CEST 2009

As a followup to http://list.seqfan.eu/pipermail/seqfan/2009-October/002522.html :

One could in principle trace this back via page A.490 of the Plouffe thesis
(as available from the OEIS link), if it would be clear which journal TR
is (Transcations of the Am. Math Soc?, but this does not have anything
on page 73 of its July 1973 issue related to diophantine equations.).

So the next guess is the "Technology Review" just as quoted in the A006451,
and there may be MIT members who have access to it, but I don't:
or one could write to Allan Gottlieb who might be the author of the article,

If nobody finds an answer to this puzzle, we can proceed with the

%I A006451 M1472
%N A006451 Solutions x to the diophantine equation (2*x+1)^2 -2*(2*y)^2= -7.
%C A006451 Numbers x such that x*(x+1)/2+1 is a perfect square [Joerg Arndt, (arndt(AT)jjj.de) Oct 10 2009]
%Y A006451 Cf. A006452 (the associated y), A077446 (the 2*x+1). [R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 20 2009]

which seems to match the sequence, just a rephrasing of Joerg's proposal.

Richard Mathar

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