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A120270
The numerator of determinant of n X n matrix with elements M[i,j] = 1/(Prime[i] + Prime[j]), i,j=1..n.
0
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).
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
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jul 01 2006
STATUS
approved