A113709 a(n) is the composite between p(n) and p(n+1), where p(n) is the n-th prime, which is divisible by (p(n+1)-p(n)).
4, 6, 8, 12, 16, 18, 20, 24, 30, 36, 40, 42, 44, 48, 54, 60, 66, 68, 72, 78, 80, 84, 96, 100, 102, 104, 108, 112, 126, 128, 132, 138, 140, 150, 156, 162, 164, 168, 174, 180, 190, 192, 196, 198, 204, 216, 224, 228, 232, 234, 240, 250, 252, 258, 264, 270, 276, 280
Offset: 2
Keywords
Examples
Between the primes 67 and 71 is the composite 68 and 68 is divisible by (71-67)=4. So 68 is in the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 2..1000
Programs
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Mathematica
f[n_] := Block[{p = Prime[n], q = Prime[n + 1]}, q - Mod[p, q - p]]; Table[ f[n], {n, 2, 60}] (* Robert G. Wilson v *) cbp[{a_,b_}]:=Select[Range[a+1,b-1],Divisible[#,b-a]&]; cbp/@ Partition[ Prime[ Range[2,100]],2,1]//Flatten (* Harvey P. Dale, Jan 09 2019 *)
Formula
a(n)=p(n+1) - (p(n) (mod p(n+1)-p(n))).
Extensions
More terms from Don Reble and Robert G. Wilson v, Nov 07 2005
Comments