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

0,1

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

Links

Robert Israel, Table of n, a(n) for n = 0..355

The Prime Pages, 659*2^800516-1

Example

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

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);

Prog

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

Crossrefs

Cf. A020639, A038699, A057026.

Sequence in context: A105562 A323704 A272202 * A209195 A113222 A366671

Adjacent sequences: A244606 A244607 A244608 * A244610 A244611 A244612

Keyword

nonn

Author

Robert Israel, Jul 01 2014

Status

approved