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A052333 Riesel problem: start with n; repeatedly double and add 1 until reach a prime. Sequence gives a(n) = prime reached, or 0 if no prime is ever reached.

%I A052333 #50 Apr 29 2025 13:02:33
%S A052333 3,5,7,19,11,13,31,17,19,43,23,103,223,29,31,67,71,37,79,41,43,367,47,
%T A052333 199,103,53,223,463,59,61,127,131,67,139,71,73,151,311,79,163,83,5503,
%U A052333 738197503,89,367,751,191,97,199,101,103,211,107,109,223,113,463
%N A052333 Riesel problem: start with n; repeatedly double and add 1 until reach a prime. Sequence gives a(n) = prime reached, or 0 if no prime is ever reached.
%C A052333 Equivalently, a(n) = smallest prime of form (n+1)*2^k-1 for k >= 1, or 0 if no such prime exists.
%C A052333 a(509202) = 0 (i.e. never reaches a prime) - Chris Nash (chris_nash(AT)hotmail.com). (Of course this is related to the entry 509203 of A076337.)
%C A052333 a(73) is a 771-digit prime reached after 2552 iterations - _Warut Roonguthai_. This was proved to be a prime by Paul Jobling (Paul.Jobling(AT)WhiteCross.com) using PrimeForm and by _Ignacio Larrosa Cañestro_ using Titanix (http://www.znz.freesurf.fr/pages/titanix.html). [Oct 30 2000]
%H A052333 N. J. A. Sloane, <a href="/A052333/b052333.txt">Table of n, a(n) for n = 1..657</a>. Note that A050412(658) = 800516, so a(658) has 240983 digits, which is too large for a b-file.
%H A052333 Ray Ballinger and Wilfrid Keller, <a href="http://www.prothsearch.com/rieselprob.html">The Riesel Problem: Definition and Status</a>
%H A052333 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 A052333 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%e A052333 a(4)=19 because 4 -> 9 (composite) -> 19 (prime).
%t A052333 Table[NestWhile[2#+1&,2n+1,!PrimeQ[#]&,1,1000],{n,60}] (* _Harvey P. Dale_, May 08 2011 *)
%o A052333 (PARI) a(n)=while(!isprime(n=2*n+1),);n \\ oo loop when a(n) = 0. - _Charles R Greathouse IV_, May 08 2011
%Y A052333 CMain sequences for Riesel problem: A038699, A040081, A046069, A050412, A052333, A076337, A101036, A108129.
%Y A052333 Cf. A051914, A052334, A052339, A052340, A040081.
%K A052333 nonn,nice
%O A052333 1,1
%A A052333 _Christian G. Bower_, Dec 19 1999