A113729 a(n) is the integer between p(n) and p(n+3) which is divisible by (p(n+3)-p(n)), where p(n) is the n-th prime.

5, 8, 8, 10, 16, 20, 24, 24, 28, 36, 36, 40, 48, 48, 56, 56, 60, 72, 72, 72, 80, 90, 90, 98, 100, 104, 110, 120, 110, 120, 132, 144, 140, 144, 154, 160, 160, 176, 168, 180, 182, 192, 192, 198, 208, 224, 216, 230, 228, 240, 234, 252, 242, 252, 266, 266, 276, 276

Offset

1,1

Comments

Exactly one integer exists between each p(n+3) and p(n) which is divisible by (p(n+3)-p(n)).

Links

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

Formula

a(n)=p(n+3) - (p(n) (mod p(n+3)-p(n))).

Example

Between the primes 19 and 31 is the composite 24 and 24 is divisible by (31-19)=12. So 24 is in the sequence.

Mathematica

f[n_] := Block[{p = Prime[n], q = Prime[n + 3]}, q - Mod[p, q - p]]; Table[ f[n], {n, 58}] (* Robert G. Wilson v *)
id[{a_, b_, c_, d_}]:=Select[Range[a+1, d-1], Divisible[#, d-a]&]; Flatten[ id/@ Partition[Prime[Range[70]], 4, 1]] (* Harvey P. Dale, May 07 2015 *)

Crossrefs

Cf. A113709, A113728.

Sequence in context: A073822 A198606 A031165 * A097523 A250123 A335298

Adjacent sequences: A113726 A113727 A113728 * A113730 A113731 A113732

Keyword

nonn

Author

Leroy Quet, Nov 08 2005

Extensions

More terms from Robert G. Wilson v, Nov 09 2005

Status

approved