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

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, 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, 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

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

There exist odd integers 2k-1 such that (2k-1)2^n-1 is always composite.

References

• Ribenboim, P., The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Hans Riesel, Some large prime numbers. Translated from the Swedish original (Några stora primtal, Elementa 39 (1956), pp. 258-260) by Lars Blomberg.
• Eric Weisstein's World of Mathematics, Riesel Number.

Crossrefs

Main sequences for Riesel problem: A038699, A040081, A046069, A050412, A052333, A076337, A101036, A108129.

Cf. A046067, A046070.

Bisection of A040081.

Programs

Mathematica

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 *)