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

2,1

Comments

Exactly one composite exists between each p(n+1) and p(n) which is divisible by (p(n+1)-p(n)), for n >= 2.

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Formula

a(n)=p(n+1) - (p(n) (mod p(n+1)-p(n))).

Example

Between the primes 67 and 71 is the composite 68 and 68 is divisible by (71-67)=4. So 68 is in the sequence.

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 *)

Crossrefs

Cf. A113710, A111379.

Sequence in context: A199768 A157932 A097619 * A076082 A162648 A225512

Adjacent sequences: A113706 A113707 A113708 * A113710 A113711 A113712

Keyword

nonn

Author

Leroy Quet, Nov 06 2005

Extensions

More terms from Don Reble and Robert G. Wilson v, Nov 07 2005

Status

approved