A127852 Numbers n such that A118679(n) = 1.

1, 3, 10, 19, 24, 30, 43, 51, 58, 62, 73, 75, 82, 94, 101, 106, 115, 116, 118, 128, 138, 147, 149, 159, 160, 163, 167, 172, 183, 186, 190, 191, 195, 201, 211, 214, 219, 249, 250, 252, 253, 260, 266, 272, 274, 277, 279, 283, 290, 294, 296, 306, 309, 310, 318

Offset

1,2

Comments

A118679[ a(n) ] = 1, where A118679(n) = {1, 2, 1, 13, 19, 13, 17, 43, 53, 1, 19, ...} = Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1. A118679(n) = Numerator[ (n^2+3n-2)/(2(n+1)!) ] = Numerator[ ((2n+3)^2-17)/(4(n+1)!) ].

Links

Table of n, a(n) for n=1..55.

Formula

An integer n is in this sequence iff all prime divisors of n^2+3n-2 do not exceed n+1 and n^2+3n-2 is not of the form 2*p^2 for some prime p. [From Max Alekseyev, Jun 02 2009]

Mathematica

Select[Range[1000], Numerator[(#^2+3#-2)/(2(#+1)!)]==1&]

Crossrefs

Cf. A118679, A118680, A127853.

Sequence in context: A074893 A074178 A178996 * A064027 A321543 A212456

Adjacent sequences: A127849 A127850 A127851 * A127853 A127854 A127855

Keyword

nonn

Author

Alexander Adamchuk, Feb 03 2007

Status

approved