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
Keywords
Examples
Between the primes 19 and 31 is the composite 24 and 24 is divisible by (31-19)=12. So 24 is in the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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 *)
Formula
a(n)=p(n+3) - (p(n) (mod p(n+3)-p(n))).
Extensions
More terms from Robert G. Wilson v, Nov 09 2005
Comments