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A046069 Riesel Problem: Smallest m >= 0 such that (2n-1)2^m-1 is prime, or -1 if no such value exists.

%I A046069 #19 Feb 16 2025 08:32:38
%S A046069 2,0,2,1,1,2,3,1,2,1,1,4,3,1,4,1,2,2,1,3,2,7,1,4,1,1,2,1,1,12,3,2,4,5,
%T A046069 1,2,7,1,2,1,3,2,5,1,4,1,3,2,1,1,10,3,2,10,9,2,8,1,1,12,1,2,2,25,1,2,
%U A046069 3,1,2,1,1,2,5,1,4,5,3,2,1,1,2,3,2,4,1,2,2,1,1,8,3,4,2,1,3,226,3,1,2
%N A046069 Riesel Problem: Smallest m >= 0 such that (2n-1)2^m-1 is prime, or -1 if no such value exists.
%C A046069 There exist odd integers 2k-1 such that (2k-1)2^n-1 is always composite.
%D A046069 Ribenboim, P., The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.
%H A046069 T. D. Noe, <a href="/A046069/b046069.txt">Table of n, a(n) for n=1..1000</a>
%H A046069 Hans Riesel, <a href="/A076337/a076337.pdf">Some large prime numbers</a>. Translated from the Swedish original (Några stora primtal, Elementa 39 (1956), pp. 258-260) by Lars Blomberg.
%H A046069 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RieselNumber.html">Riesel Number.</a>
%t A046069 max = 10^6; (* this maximum value of m is sufficient up to n=1000 *) a[1] = 2; a[2] = 0; a[n_] := For[m = 1, m <= max, m++, If[PrimeQ[(2*n - 1)*2^m - 1], Return[m]]] /. Null -> -1; Reap[ Do[ Print[ "a(", n, ") = ", a[n]]; Sow[a[n]], {n, 1, 100}]][[2, 1]] (* _Jean-François Alcover_, Nov 15 2013 *)
%Y A046069 Main sequences for Riesel problem: A038699, A040081, A046069, A050412, A052333, A076337, A101036, A108129.
%Y A046069 Cf. A046067, A046070.
%Y A046069 Bisection of A040081.
%K A046069 nonn
%O A046069 1,1
%A A046069 _Eric W. Weisstein_