A046069 - OEIS

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

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OFFSET

1,1

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.

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 *)

CROSSREFS

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

Cf. A046067, A046070.

Bisection of A040081.

Sequence in context: A029399 A302172 A249338 * A320042 A055651 A175929

Adjacent sequences: A046066 A046067 A046068 * A046070 A046071 A046072

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved