A248626 Least positive integer m such that prime(m+n) divides 2^m - 1.

3, 22, 18, 50, 48, 5, 48, 121, 390, 21, 37, 9, 11, 110, 672, 11628, 14, 286, 1000, 329, 15, 29, 32, 7, 90, 42, 1001, 816, 24, 408, 806, 6219, 761, 44, 75, 88, 30, 711, 16, 43, 2202, 110, 6112, 624, 12206, 590, 21, 156, 551, 525, 194, 64, 201, 225, 261, 1132, 305, 66, 500, 50

Offset: 1

Author

Zhi-Wei Sun, Oct 10 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for any n > 0.

Examples

			a(2) = 22 since prime(22+2) = 89 divides 2^(22)-1 = 4194303 = 89*47127.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..9844 (n = 1..587 from Zhi-Wei Sun)

Crossrefs

Cf. A000040, A000225, A248588.

Programs

Mathematica

Do[m=1;Label[aa];If[Mod[2^m-1,Prime[m+n]]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]