A068901 Least number that when added to the n-th prime gives a multiple of n.

0, 1, 1, 1, 4, 5, 4, 5, 4, 1, 2, 11, 11, 13, 13, 11, 9, 11, 9, 9, 11, 9, 9, 7, 3, 3, 5, 5, 7, 7, 28, 29, 28, 31, 26, 29, 28, 27, 28, 27, 26, 29, 24, 27, 28, 31, 24, 17, 18, 21, 22, 21, 24, 19, 18, 17, 16, 19, 18, 19, 22, 17, 8, 9, 12, 13, 4, 3, 67, 1

Offset: 1

Author

Reinhard Zumkeller, Mar 05 2002

Keywords

• nonn
• nice
• look

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A090973. - Reinhard Zumkeller, Aug 16 2009

Cf. A000040, A068902.

Programs

Haskell

a068901 n = head $
   filter ((== 0) . (`mod` fromIntegral n) . (+ a000040 n)) $ [0..]
-- Reinhard Zumkeller, Feb 18 2012

Mathematica

f[n_] := Module[{p=Prime[n]}, n*Ceiling[p/n]-p]; Array[f,100]  (* Harvey P. Dale, Apr 06 2011 *)

Formula

a(n) = Min_{k | n divides (prime(n)+k)}.

a(n) = A068902(n) - A000040(n).

a(n) = n*ceiling(prime(n)/n) - prime(n). - Vladeta Jovovic, Apr 06 2003