login
Least number that when added to the n-th prime gives a multiple of n.
6

%I #28 Jul 31 2023 02:55:33

%S 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,

%T 28,29,28,31,26,29,28,27,28,27,26,29,24,27,28,31,24,17,18,21,22,21,24,

%U 19,18,17,16,19,18,19,22,17,8,9,12,13,4,3,67,1

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

%H Reinhard Zumkeller, <a href="/A068901/b068901.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F a(n) = n*ceiling(prime(n)/n) - prime(n). - _Vladeta Jovovic_, Apr 06 2003

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

%o (Haskell)

%o a068901 n = head $

%o filter ((== 0) . (`mod` fromIntegral n) . (+ a000040 n)) $ [0..]

%o -- _Reinhard Zumkeller_, Feb 18 2012

%Y Cf. A090973. - _Reinhard Zumkeller_, Aug 16 2009

%Y Cf. A000040, A068902.

%K nonn,nice,look

%O 1,5

%A _Reinhard Zumkeller_, Mar 05 2002