A248590 Least positive integer m such that prime(m) == 1 (mod m + n).

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, 30, 13, 14, 599, 97, 15, 31, 32, 178, 33, 16, 102, 104, 35, 108, 17, 18, 38, 39, 361, 40, 19, 41, 73, 20, 21, 43, 45, 78, 134, 22, 391, 47, 23, 84

Offset: 1

Author

Zhi-Wei Sun, Oct 09 2014

Keywords

• nonn

Comments

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

(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.

Examples

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

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A247824, A248004, A248588.

Programs

Mathematica

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}]