A248590 - OEIS

%I #7 Oct 09 2014 09:49:08

%S 3,4,19,10,5,6,13,15,7,8,31,17,9,19,20,38,22,10,11,24,78,80,25,12,28,

%T 30,13,14,599,97,15,31,32,178,33,16,102,104,35,108,17,18,38,39,361,40,

%U 19,41,73,20,21,43,45,78,134,22,391,47,23,84

%N Least positive integer m such that prime(m) == 1 (mod m + n).

%C Conjecture: (i) a(n) exists for any n > 0. Moreover, a(n) < n*(n-1) if n > 3.

%C (ii) For any n > 0, there is a positive integer m such that prime(m) == -1 (mod m + n). Moreover, we may require m < n*(n-1) if n > 1.

%H Zhi-Wei Sun, <a href="/A248590/b248590.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 19 since prime(19) = 67 == 1 (mod 19 + 3).

%t Do[m=1;Label[aa];If[Mod[Prime[m]-1,m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

%Y Cf. A000040, A247824, A248004, A248588.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Oct 09 2014