A101328 Recurring numbers in the count of consecutive composite numbers between balanced primes and their lower or upper prime neighbors.

1, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 203, 209, 215, 221, 227, 233, 239, 245, 251, 257, 263, 269, 275, 281, 287, 293, 299, 305, 311, 317, 323, 329

Offset

2,2

Comments

Except for the initial term, these numbers appear to differ by 6. Proof?

Numbers that occur in A101597. - David Wasserman, Mar 26 2008

Links

Table of n, a(n) for n=2..57.

Formula

If the numbers continue to differ by 6, then this is the sum of paired terms of 3n+1: (1, 4, 7, 10, 13, ...); and binomial transform of [1, 4, 2, -2, 2, -2, 2, ...]. - Gary W. Adamson, Sep 13 2007

a(n) = nextprime(A054342(n)+1)-A054342(n)-1. - David Wasserman, Mar 26 2008

Crossrefs

Cf. A016969, A054342, A101597.

Conjectured partial sums of A329502.

Sequence in context: A314254 A059538 A172337 * A016969 A358528 A007528

Adjacent sequences: A101325 A101326 A101327 * A101329 A101330 A101331

Keyword

nonn

Author

Cino Hilliard, Jan 26 2005

Extensions

More terms from David Wasserman, Mar 26 2008

Status

approved