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A250205 Riesel problem in base 6: Least k > 0 such that n*6^k-1 is prime, or 0 if no such k exists.

%I A250205 #34 Mar 20 2015 05:26:28
%S A250205 1,1,1,1,1,0,1,1,1,1,0,1,2,1,1,0,1,1,1,2,0,1,1,2,1,0,2,1,1,1,0,1,1,2,
%T A250205 2,0,4,1,1,1,0,1,1,1,1,0,1,4,1,3,0,1,1,6,2,0,5,1,1,1,0,6,2,1,1,0,1,2,
%U A250205 10,1,0,1,3,1,1,0,1,1,2,1,0,1,8,1,1,0,1,2,2,4,0,49,1,1,1,0,2,1,1,1,0,2,1,6,2,0,1,1,1,1,0,5,1,1,2,0,1,10,2,1
%N A250205 Riesel problem in base 6: Least k > 0 such that n*6^k-1 is prime, or 0 if no such k exists.
%C A250205 a(5j+1) = 0 except for a(1), since (5j+1)*6^k-1 is always divisible by 5, but there are infinitely many numbers not in the form 5j+1 such that a(n) = 0.
%C A250205 a(n) = 0 for n == 84687 mod 10124569, because then n*6^k-1 is always divisible by at least one of 7, 13, 31, 37, 97. - _Robert Israel_, Mar 17 2015
%C A250205 Conjecture: if n is not in the form 5j+1 and n < 84687, then a(n) > 0.
%H A250205 Eric Chen, <a href="/A250205/b250205.txt">Table of n, a(n) for n = 1..1000</a>
%H A250205 Gary Barnes, <a href="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm">Riesel conjectures and proofs</a>
%F A250205 a(A024898(n)) = 1. - _Michel Marcus_, Mar 16 2015
%p A250205 N:= 1000: # to get a(1) to a(N), using k up to 10000
%p A250205 a[1]:= 1:
%p A250205 for n from 2 to N do
%p A250205 if n mod 5 = 1 then a[n]:= 0
%p A250205 else
%p A250205     for k from 1 to 10000 do
%p A250205     if isprime(n*6^k-1) then
%p A250205        a[n]:= k;
%p A250205          break
%p A250205       fi
%p A250205     od
%p A250205 fi
%p A250205 od:
%p A250205 seq(a[n],n=1..N); # _Robert Israel_, Mar 17 2015
%t A250205 (* m <= 10000 is sufficient up to n = 1000 *)
%t A250205 a[n_] := For[k = 1, k <= 10000, k++, If[PrimeQ[n*6^k - 1], Return[k]]] /. Null -> 0; Table[a[n], {n, 1, 120}]
%o A250205 (PARI) a(n) = if(n%5==1 && n>1, 0, for(k = 1, 10000, if(ispseudoprime(n*6^k-1), return(k))))
%Y A250205 Cf. A040081, A046069, A050412, A108129.
%Y A250205 Cf. A250204 (Least k > 0 such that n*6^k+1 is prime).
%K A250205 nonn
%O A250205 1,13
%A A250205 _Eric Chen_, Mar 13 2015