cp's OEIS Frontend

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.

A349496 Numbers of the form 4*t^2-2 (A060626) when t >= 1 is an integer that is not a term in A001542.

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%I A349496 #23 Nov 28 2021 05:19:06
%S A349496 2,34,62,98,142,194,254,322,398,482,674,782,898,1022,1154,1294,1442,
%T A349496 1598,1762,1934,2114,2302,2498,2702,2914,3134,3362,3598,3842,4094,
%U A349496 4354,4622,4898,5182,5474,5774,6082,6398,6722,7054,7394,7742,8098,8462,8834,9214,9602,9998,10402
%N A349496 Numbers of the form 4*t^2-2 (A060626) when t >= 1 is an integer that is not a term in A001542.
%C A349496 Equivalently: numbers k for which there exists only one integer m with here m = k/2 + 1 such that A000178(k) / m! is a square, where A000178(k) = k$ = 1!*2!*...*k! is the superfactorial of k.
%H A349496 Rick Mabry and Laura McCormick, <a href="https://www.austms.org.au/wp-content/uploads/Gazette/2009/Nov09/TechPaperMabry.pdf">Square products of punctured sequences of factorials</a>, Gaz. Aust. Math. Soc., 2009, pages 346-352 (FFF 2. (3) p. 348).
%e A349496 A060626(3) = 34 and 3 is not a term in A001542; also 34$ / 18! is a square, hence 34 is a term.
%o A349496 (PARI) isok(m) = my(x=(m+2)/4, y); issquare(x, &y) && (denominator(y)==1) && !issquare(2*x+1); \\ _Michel Marcus_, Nov 22 2021
%Y A349496 Cf. A000178, A001542, A348692, A349079.
%Y A349496 Subsequence of A060626 and of A349080.
%K A349496 nonn
%O A349496 1,1
%A A349496 _Bernard Schott_, Nov 21 2021