A060359 a(n) = (smallest prime > k) - (largest prime < k), where k = lcm(1..n).

2, 2, 2, 2, 2, 14, 18, 18, 32, 32, 54, 54, 54, 40, 62, 62, 2, 2, 2, 2, 42, 42, 30, 30, 72, 72, 44, 44, 44, 42, 42, 42, 42, 42, 96, 96, 96, 96, 126, 126, 142, 142, 142, 142, 2, 2, 142, 142, 142, 142, 122, 122, 122, 122, 122, 122, 262, 262, 98, 98

Offset: 3

Author

N. J. A. Sloane, Apr 01 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1020

Crossrefs

Cf. A003418, A013633, A060357, A060358.

Programs

Maple

a:= n-> (m->nextprime(m)-prevprime(m))(ilcm($1..n)):
seq (a(n), n=3..100);

Mathematica

f[n_]:=Module[{lcmn=LCM@@Range[n]}, NextPrime[lcmn]-NextPrime[lcmn,-1]]; f/@Range[3,70]  (* Harvey P. Dale, Feb 04 2011 *)

PARI

a(n) = my(lc = lcm([1..n])); nextprime(lc+1) - precprime(lc-1); \\ Michel Marcus, Mar 20 2018

Formula

a(n) = A013633(A003418(n)). - Michel Marcus, Mar 20 2018