A244609 Least prime divisor of 659*2^n-1.

2, 3, 5, 3, 13, 3, 5, 3, 73, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 977, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 31, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 73, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 13477, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 48430237, 3, 5, 3, 7, 3, 5, 3, 13

Offset: 0

Author

Robert Israel, Jul 01 2014

Keywords

• nonn

Comments

a(n) = 3 if n is odd.

a(n) = 5 if n == 2 (mod 4).

From Bruno Berselli, Jul 02 2014: (Start)

a(n) = 7 if n == 0 (mod 12) for n>0.

a(n) = 13 if n == 4 (mod 12).

a(n) == 3 or 7 (mod 12) for n>1. (End)

A040081(659) = 800516, so 800516 is the first n for which a(n) = 659*2^n-1 (found by David W Linton in 2004). - Jens Kruse Andersen, Jul 02 2014

Examples

			For n=4, 659*2^4-1 = 10543 = 13 * 811 so a(4) = 13.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..355
• The Prime Pages, 659*2^800516-1

Crossrefs

Cf. A020639, A038699, A057026.

Programs

Magma

[PrimeDivisors(659*2^n-1)[1]: n in [0..100]]; // Bruno Berselli, Jul 02 2014

Maple

f:= proc(m) local F;
   F:= map(t -> t[1],ifactors(659*2^m-1,easy)[2]);
   F:= select(type,F,integer);
   if nops(F) = 0 then
     F:= map(t -> t[1],ifactors(659*2^m-1)[2]);
     min(F);
   else min(F)
   fi
end proc;
seq(f(n), n= 0 .. 100);