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

%I A244609 #25 Sep 24 2023 04:04:15
%S A244609 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 A244609 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 A244609 3,5,3,13,3,5,3,48430237,3,5,3,7,3,5,3,13
%N A244609 Least prime divisor of 659*2^n-1.
%C A244609 a(n) = 3 if n is odd.
%C A244609 a(n) = 5 if n == 2 (mod 4).
%C A244609 From _Bruno Berselli_, Jul 02 2014: (Start)
%C A244609 a(n) = 7 if n == 0 (mod 12) for n>0.
%C A244609 a(n) = 13 if n == 4 (mod 12).
%C A244609 a(n) == 3 or 7 (mod 12) for n>1. (End)
%C A244609 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 A244609 Robert Israel, <a href="/A244609/b244609.txt">Table of n, a(n) for n = 0..355</a>
%H A244609 The Prime Pages, <a href="https://t5k.org/primes/page.php?id=69058">659*2^800516-1</a>
%e A244609 For n=4, 659*2^4-1 = 10543 = 13 * 811 so a(4) = 13.
%p A244609 f:= proc(m) local F;
%p A244609    F:= map(t -> t[1],ifactors(659*2^m-1,easy)[2]);
%p A244609    F:= select(type,F,integer);
%p A244609    if nops(F) = 0 then
%p A244609      F:= map(t -> t[1],ifactors(659*2^m-1)[2]);
%p A244609      min(F);
%p A244609    else min(F)
%p A244609    fi
%p A244609 end proc;
%p A244609 seq(f(n), n= 0 .. 100);
%o A244609 (Magma) [PrimeDivisors(659*2^n-1)[1]: n in [0..100]]; // _Bruno Berselli_, Jul 02 2014
%Y A244609 Cf. A020639, A038699, A057026.
%K A244609 nonn
%O A244609 0,1
%A A244609 _Robert Israel_, Jul 01 2014