A118335 a(n)= smallest multiple of (prime(n+1)-prime(n)) which is >= prime(n+1), where prime(m) is the m-th prime.

3, 6, 8, 12, 14, 20, 20, 24, 30, 32, 42, 44, 44, 48, 54, 60, 62, 72, 72, 74, 84, 84, 90, 104, 104, 104, 108, 110, 116, 140, 132, 138, 140, 150, 152, 162, 168, 168, 174, 180, 182, 200, 194, 200, 200, 216, 228, 228, 230, 236, 240, 242, 260, 258, 264, 270, 272, 282

Offset: 1

Author

Leroy Quet, Apr 25 2006

Keywords

• nonn

Comments

a(n) < a(n-1) for n: 31,43,54,83,98,100,116,122,140,142,155,163,169,173,178,..., . - Robert G. Wilson v, Apr 27 2006

Crossrefs

Cf. A113709, A118336.

Programs

Mathematica

f[n_] := Block[{m = Prime[n + 1] - Prime[n]}, k = Mod[m, Prime[n + 1]]; While[k < Prime[n + 1], k += m]; k]; Array[f, 58] (* Robert G. Wilson v, Apr 27 2006 *)

Formula

a(n) - A118336(n) = 2 *(prime(n+1) - prime(n)).

a(n) - A113709(n) = prime(n+1) - prime(n), for n>= 2.

Extensions

More terms from Robert G. Wilson v, Apr 27 2006