|
Search: id:A120292
|
|
|
| A120292 |
|
Absolute value of numerator of determinant of n X n matrix with elements M[i,j] = Prime[i]/(1+Prime[i]) if i=j and 1 otherwise. |
|
+0
5
|
|
| 2, 1, 1, 5, 1, 23, 1, 1, 1, 23, 17, 13, 5, 1, 1, 1, 1, 37, 293, 47, 61, 29, 1, 29, 271, 593, 43, 233, 29, 811, 1, 941, 101, 1, 1, 1231, 131, 29, 1, 521, 1, 109, 1, 149, 509, 89, 59, 107, 617, 1, 1, 47, 173, 3067, 47, 1, 3463, 3599, 89, 431, 4021, 521, 2161, 2239, 103, 1, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Some a(n) are equal to 1 (n=2,3,5,7,8,9,14,15,16,17,23,31,34,35,39,41,43,50,51,56,..).
a(58)=3599=59*61 is not prime. - T. D. Noe (noe(AT)sspectra.com), Nov 15 2006
Most terms are prime or 1.
Numbers n such that A120292(n)>1 and is not prime are listed in A141779(n) = {58, 282, 367, 743, 808, 1015, 1141, 1299, 1962, 2109, 2179, 2397, 2501, ...}.
Nonprime terms that are greater than 1 are listed in A141781(n) = {3599, 118477, 210589, 971573, 1164103, 1901959, 2446681, 3230069, ...}.
Note that all listed terms of A141781(n) are semiprime, for example: 3599 = 59*61, 118477 = 257*461, 210589 = 251*839, 971573 = 643*1511.
Conjecture: All nonprime terms that are greater than 1 are semiprime.
|
|
LINKS
|
Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2008, Table of n, a(n) for n = 1..282
|
|
FORMULA
|
a(n) = Abs[numerator[Det[DiagonalMatrix[Table[Prime[i]/(Prime[i]+1)-1,{i,1,n}]]+1]]].
a(n) = Numerator[Abs[(-1)^n*(1 - Sum[Prime[k] + 1,{k, 1, n}])/Product[Prime[k] + 1, {k, 1, n}] ]],{n,1,282}]
|
|
MATHEMATICA
|
Abs[Numerator[Table[Det[DiagonalMatrix[Table[Prime[i]/(Prime[i]+1)-1, {i, 1, n}]]+1], {n, 1, 60}]]]
Table[Numerator[Abs[(1 - Sum[Prime[k] + 1, {k, 1, n}])/Product[Prime[k] + 1, {k, 1, n}] ]], {n, 1, 282}]
|
|
CROSSREFS
|
Cf. A024528, A118679.
Cf. A125716 = Numbers n such that A120292(n) = 1. Cf. A141780 = Numbers n such that A120292(n) is prime. Cf. A141779 = Numbers n such that A120292(n)>1 and is not prime. Cf. A141781 = Terms of A120292(n) that are greater than 1 and are not prime; or A120292( A141779(n) ).
Adjacent sequences: A120289 A120290 A120291 this_sequence A120293 A120294 A120295
Sequence in context: A141323 A136789 A022661 this_sequence A128604 A098885 A106270
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 08 2006, Jul 04 2008
|
|
|
Search completed in 0.002 seconds
|
