A120270 The numerator of determinant of n X n matrix with elements M[i,j] = 1/(Prime[i] + Prime[j]), i,j=1..n.

1, 1, 3, 1, 1, 11, 1, 17, 1, 1, 29, 29, 1, 41, 41, 4913, 17, 59, 59, 1, 71, 71, 1, 1, 1, 1, 101, 101, 10807, 1, 1, 1, 1, 137, 137, 20413, 20413, 20413, 1, 1, 1, 179, 1, 191, 191, 37627, 37627, 37627, 191, 43357, 227, 227, 54253, 227, 1, 1, 1, 269, 269, 1

Offset

1,3

Comments

Many a(n) are equal to 1. It appeares that almost all other a(n) are primes that belong to the Lesser of Twin Primes A001359(k) or equal to the product of two primes from A001359(k), mostly consecutive. a(16) = 17^3 is an exception - it is a cube of a prime from A001359(k). All lesser twin primes from A001359(k) except 5 appear in a(n) for the first time in their natural order. 5 is the only lesser twin prime that does not appear in a(n). If p=Prime[n]>5 is lesser of twin primes then p divides a(n+1).

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = numerator[ Det[ 1/(Prime[i] + Prime[j]), {i,1,n},{j,1,n} ]].

Example

Matrix begins
1/4 1/5 1/7 1/9 ...
1/5 1/6 1/8 1/10 ...
1/7 1/8 1/10 1/12 ...
1/9 1/10 1/12 1/14 ...
...

Mathematica

Numerator[Table[Det[Table[1/(Prime[i]+Prime[j]), {i, 1, n}, {j, 1, n}]], {n, 1, 60}]]

Crossrefs

Cf. A001359.

Sequence in context: A086766 A078688 A082466 * A243752 A113711 A339019

Adjacent sequences: A120267 A120268 A120269 * A120271 A120272 A120273

Keyword

frac,nonn

Author

Alexander Adamchuk, Jul 01 2006

Status

approved