|
| |
|
|
A118679
|
|
Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.
|
|
17
| |
|
|
1, 2, 1, 13, 19, 13, 17, 43, 53, 1, 19, 89, 103, 59, 67, 151, 13, 47, 1, 229, 251, 137, 149, 1, 349, 47, 101, 433, 463, 1, 263, 43, 593, 157, 83, 701, 739, 389, 409, 859, 53, 59, 1, 1033, 83, 563, 587, 1223, 67, 331, 1, 1429, 1483, 769, 797, 127, 1709, 1, 457, 1889
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Numbers n such that a(n) = 1 are listed in A127852.
All a(n)>1 are prime belonging to A038889 (i.e., 17 is a square mod a(n)).
|
|
|
FORMULA
| det(M) = (-1)^(n+1)*(n^2+3*n-2)/(2*(n+1)!), implying that a(n)=p, where p=A006530(n^2+3*n-2) is the largest prime divisor of (n^2+3*n-2), if p>n+1 or p=sqrt((n^2+3*n-2)/2); otherwise a(n)=1.
a(n) = Numerator[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ]].
a(n) = Numerator[ (n^2+3n-2)/(2(n+1)!) ] = Numerator[ ((2n+3)^2-17)/(4(n+1)!) ].
|
|
|
MATHEMATICA
| Numerator[Table[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ], {n, 1, 70} ]]
Table[ Numerator[ (n^2+3n-2)/(2(n+1)!) ], {n, 1, 100} ]
|
|
|
CROSSREFS
| Cf. A038889.
Cf. A118680, A127852, A127853.
Sequence in context: A074808 A113097 A032001 * A087451 A063558 A174170
Adjacent sequences: A118676 A118677 A118678 * A118680 A118681 A118682
|
|
|
KEYWORD
| frac,nonn
|
|
|
AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), May 19 2006, Feb 03 2007
|
|
|
EXTENSIONS
| Edited by Max Alekseyev (maxale(AT)gmail.com), Jun 02 2009
|
| |
|
|
