A113728 a(n) is the integer between p(n) and p(n+2) which is divisible by (p(n+2)-p(n)), where p(n) is the n-th prime.

3, 4, 6, 12, 12, 18, 18, 20, 24, 32, 40, 42, 42, 50, 48, 56, 64, 70, 72, 72, 80, 80, 84, 96, 102, 102, 108, 108, 126, 126, 130, 136, 144, 144, 152, 156, 160, 170, 168, 176, 180, 192, 192, 198, 210, 216, 224, 228, 228, 230, 240, 240, 256, 252, 264, 264, 272, 280

Offset

1,1

Comments

Exactly one integer exists between each p(n+2) and p(n) which is divisible by (p(n+2)-p(n)).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A031131(n)*ceiling(A000040(n)/A031131(n)). - R. J. Mathar, Aug 31 2007

Example

Between the primes 19 and 29 is the composite 20 and 20 is divisible by (29-19)=10. So 20 is in the sequence.

Mathematica

For[n = 1, n < 50, n++, s := Prime[n] + 1; While[Floor[s/(Prime[n + 2] -Prime[n])] != s/(Prime[n + 2] - Prime[n]), s++ ]; Print[s]] (* Stefan Steinerberger, Feb 10 2006 *)
idp[n_]:=Module[{p1=Prime[n], p2=Prime[n+2]}, Select[Range[p1+1, p2-1], Divisible[ #, p2-p1]&]]; Table[idp[n], {n, 60}]//Flatten (* Harvey P. Dale, May 30 2021 *)

Crossrefs

Cf. A113709, A113729.

Sequence in context: A062822 A175894 A175029 * A000114 A310006 A294144

Adjacent sequences: A113725 A113726 A113727 * A113729 A113730 A113731

Keyword

nonn

Author

Leroy Quet, Nov 08 2005

Extensions

More terms from Stefan Steinerberger, Feb 10 2006

More terms from R. J. Mathar, Aug 31 2007

Status

approved