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

Author

Leroy Quet, Nov 08 2005

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A113709, A113729.

Programs

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 *)

Formula

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

Extensions

More terms from Stefan Steinerberger, Feb 10 2006

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