cp's OEIS Frontend

A046067 Smallest m such that (2n-1)2^m+1 is prime, or -1 if no such value exists.

%I A046067 #57 Aug 11 2025 08:37:07
%S A046067 0,1,1,2,1,1,2,1,3,6,1,1,2,2,1,8,1,1,2,1,1,2,2,583,2,1,1,4,2,5,4,1,1,
%T A046067 2,1,3,2,1,3,2,1,1,4,2,1,8,2,1,2,1,3,16,1,3,6,1,1,2,3,1,8,6,1,2,3,1,4,
%U A046067 1,3,2,1,53,6,8,3,4,1,1,8,6,3,2,1,7,2,8,1,2,2,1,4,1,3,6,1,1,2,4,15,2
%N A046067 Smallest m such that (2n-1)2^m+1 is prime, or -1 if no such value exists.
%C A046067 There exist odd integers 2k-1 such that (2k-1)2^n+1 is always composite.
%C A046067 The smallest known example is 78557. Therefore a(39279) = -1.
%C A046067 For the corresponding primes see A057025(n-1), n >= 1, where a 0 will show up if a(n) = -1. - _Wolfdieter Lang_, Feb 07 2013.
%C A046067 Jaeschke shows that every positive integer appears infinitely often. - _Jeppe Stig Nielsen_, Jul 06 2020
%D A046067 Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.
%H A046067 T. D. Noe, <a href="/A046067/b046067.txt">Table of n, a(n) for n = 1..5000</a> (with help from the Sierpiński problem website; typo in a(3707)=1 corrected by Jeppe Stig Nielsen)
%H A046067 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/sierp.html">Sierpiński Problem</a>
%H A046067 John R. Cowles and Ruben Gamboa, <a href="http://arxiv.org/abs/1110.4671">Verifying Sierpiński and Riesel Numbers in ACL2</a>, arXiv preprint arXiv:1110.4671 [cs.DM], 2011.
%H A046067 G. Jaeschke, <a href="http://www.jstor.org/stable/2007382">On the Smallest k Such that All k*2^N + 1 are Composite</a>, Mathematics of Computation, Vol. 40, No. 161 (Jan., 1983), pp. 381-384.
%H A046067 Seventeen or Bust, <a href="http://www.seventeenorbust.com">A Distributed Attack on the Sierpiński Problem</a>
%H A046067 W. Sierpiński, <a href="https://gdz.sub.uni-goettingen.de/id/PPN378850199_0015">Sur un problème concernant les nombres k*2^n+1</a>, Elem. d. Math. 15, pp. 73-74, 1960.
%H A046067 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RieselNumber.html">Riesel Number.</a>
%H A046067 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiNumberoftheSecondKind.html">Sierpiński Number of the Second Kind.</a>
%t A046067 max = 10000 (* this maximum value of m is sufficient up to n = 1000 *); a[n_] := For[m = 1, m <= max, m++, If[PrimeQ[(2n - 1)*2^m + 1], Return[m]]] /. Null -> -1; a[1] = 0; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jun 08 2012 *)
%Y A046067 Cf. A046068.
%Y A046067 Bisection of A040076. Cf. A033809.
%Y A046067 Cf. A057192, A057025.
%K A046067 sign
%O A046067 1,4
%A A046067 _Eric W. Weisstein_