A244609 - OEIS

%I #25 Sep 24 2023 04:04:15

%S 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,

%T 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,

%U 3,5,3,13,3,5,3,48430237,3,5,3,7,3,5,3,13

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

%C a(n) = 3 if n is odd.

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

%C From _Bruno Berselli_, Jul 02 2014: (Start)

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

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

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

%C 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

%H Robert Israel, <a href="/A244609/b244609.txt">Table of n, a(n) for n = 0..355</a>

%H The Prime Pages, <a href="https://t5k.org/primes/page.php?id=69058">659*2^800516-1</a>

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

%p f:= proc(m) local F;

%p    F:= map(t -> t[1],ifactors(659*2^m-1,easy)[2]);

%p    F:= select(type,F,integer);

%p    if nops(F) = 0 then

%p      F:= map(t -> t[1],ifactors(659*2^m-1)[2]);

%p      min(F);

%p    else min(F)

%p    fi

%p end proc;

%p seq(f(n), n= 0 .. 100);

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

%Y Cf. A020639, A038699, A057026.

%K nonn

%O 0,1

%A _Robert Israel_, Jul 01 2014