A239938 - OEIS

%I #20 Jan 25 2016 00:03:50

%S 3,2,1,1,4,1,8,1,40,3,10,1,56,1,10,0,46,1,6,1,42,51,4,1,8,67,0,18,102,

%T 1,98,1,38,6,136,0,90,1,10,3,52,1,12,1,18,3,28,1,72,165,40,657,418,1,

%U 44,205,94,9,426,1,482,1,4,0,418,252,38,1,400,165,28,1,140

%N a(n) = least number k > 0 such that n*k^n - 1 is prime, or 0 if no such k exists.

%C a(n) = 1 iff n-1 is prime.

%C If a(n) = 0 then n is in A097764. Note the converse is not true: a(4) = 1, not 0.

%C Up to a(1000), the largest term is a(456) = 947310. The PFGW program has been used to certify all the terms up to a(1000), using the 'N+1' deterministic test. - _Giovanni Resta_, Mar 30 2014

%H Giovanni Resta, <a href="/A239938/b239938.txt">Table of n, a(n) for n = 1..1000</a>

%e 1*1^1 - 1 = 0 is not prime. 1*2^1 - 1 = 1 is not prime. 1*3^1 - 1 = 2 is prime. Thus a(1) = 3.

%t nope[n_] := n > 4 && Catch@Block[{p = 2}, While[n >= p^p, If[ IntegerQ[ n^(1/p)/p], Throw@ True]; p = NextPrime@ p]; False]; a[n_] := If[nope@ n, 0, Block[{k = 1}, While[! PrimeQ[n*k^n - 1], k++]; k]]; Array[a, 80] (* _Giovanni Resta_, Mar 30 2014 *)

%t A239938[n_] := If[n != 4 && # != 1 && GCD[n, #] != 1 &[GCD @@ FactorInteger[n][[All, -1]]], 0, NestWhile[# + 1 &, 1, Not@PrimeQ[n #^n - 1] &]]; Array[A239938, 73] (* _JungHwan Min_, Dec 28 2015 *)

%o (PARI) Pro(n) = for(k=1,10^4,if(ispseudoprime(n*k^n-1),return(k)));

%o n=1; while(n<100,print1(Pro(n), ", ");n+=1)

%Y Cf. A066049, A097764, A239787.

%K nonn

%O 1,1

%A _Derek Orr_, Mar 29 2014