A110492 Number of values of k for k=1,2,3,...,n-1, such that n+k divides prime(n)+prime(k), where prime(n) denotes the n-th prime.

0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 2, 1, 2, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 2, 7, 4, 7, 8, 8, 5, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 3, 4, 5, 1, 5, 4, 8, 0, 0, 0, 0, 0, 0

Offset

1,5

Comments

Surprisingly, the nonzero terms of the sequence seem to occur in well-defined intervals separated by increasingly long intervals of zero terms, with the position of one nonzero interval located at a value of n approximately 2.4 times that of the previous one. See the link for a graph of {a(n)} vs. Log(n) to the base 2.4, for n in {1,2,...,5000}. Further,each of the integer quotients (Prime[n]+ Prime[k])/(n+k) are the same throughout each interval of nonzero values of a(n) and in fact the values of the quotients are precisely the ordinal of that interval of nonzero values.

Links

Table of n, a(n) for n=1..105.

John W. Layman, View the graph of {a(n)} vs. log(n) to the base 2.4.

Example

The first five primes are 2,3,5,7,11. We find that 5+1 does not divide 11+2, but 5+2 divides 11+3, 5+3 divides 11+5 and 5+4 divides 11+7. Therefore a(5)=3.

Crossrefs

Cf. A000040.

Sequence in context: A334885 A318330 A199261 * A225413 A180995 A144331

Adjacent sequences: A110489 A110490 A110491 * A110493 A110494 A110495

Keyword

nonn

Author

John W. Layman, Jul 22 2005

Status

approved