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

2, 34, 62, 98, 142, 194, 254, 322, 398, 482, 674, 782, 898, 1022, 1154, 1294, 1442, 1598, 1762, 1934, 2114, 2302, 2498, 2702, 2914, 3134, 3362, 3598, 3842, 4094, 4354, 4622, 4898, 5182, 5474, 5774, 6082, 6398, 6722, 7054, 7394, 7742, 8098, 8462, 8834, 9214, 9602, 9998, 10402

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..49.

Rick Mabry and Laura McCormick, Square products of punctured sequences of factorials, Gaz. Aust. Math. Soc., 2009, pages 346-352 (FFF 2. (3) p. 348).

Example

A060626(3) = 34 and 3 is not a term in A001542; also 34$ / 18! is a square, hence 34 is a term.

Prog

(PARI) isok(m) = my(x=(m+2)/4, y); issquare(x, &y) && (denominator(y)==1) && !issquare(2*x+1); \\ Michel Marcus, Nov 22 2021

Crossrefs

Cf. A000178, A001542, A348692, A349079.

Subsequence of A060626 and of A349080.

Sequence in context: A077310 A177051 A067130 * A337397 A263226 A200821

Adjacent sequences: A349493 A349494 A349495 * A349497 A349498 A349499

Keyword

nonn

Author

Bernard Schott, Nov 21 2021

Status

approved