[go: up one dir, main page]

login
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.
23
3, 5, 7, 19, 11, 13, 31, 17, 19, 43, 23, 103, 223, 29, 31, 67, 71, 37, 79, 41, 43, 367, 47, 199, 103, 53, 223, 463, 59, 61, 127, 131, 67, 139, 71, 73, 151, 311, 79, 163, 83, 5503, 738197503, 89, 367, 751, 191, 97, 199, 101, 103, 211, 107, 109, 223, 113, 463
OFFSET
1,1
COMMENTS
Equivalently, a(n) = smallest prime of form (n+1)*2^k-1 for k >= 1, or 0 if no such prime exists.
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.)
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]
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..657. Note that A050412(658) = 800516, so a(658) has 240983 digits, which is too large for a b-file.
Ray Ballinger and Wilfrid Keller, The Riesel Problem: Definition and Status
Hans Riesel, Some large prime numbers. Translated from the Swedish original (Några stora primtal, Elementa 39 (1956), pp. 258-260) by Lars Blomberg.
N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]
EXAMPLE
a(4)=19 because 4 -> 9 (composite) -> 19 (prime).
MATHEMATICA
Table[NestWhile[2#+1&, 2n+1, !PrimeQ[#]&], {n, 60}] (* Harvey P. Dale, May 08 2011 *) (* Will run for ever if a(n) = 0. - N. J. A. Sloane, Jul 29 2024 *)
PROG
(PARI) a(n)=while(!isprime(n=2*n+1), ); n \\ oo loop when a(n) = 0. - Charles R Greathouse IV, May 08 2011
CROSSREFS
CMain sequences for Riesel problem: A038699, A040081, A046069, A050412, A052333, A076337, A101036, A108129.
Sequence in context: A064080 A184875 A112986 * A074106 A002261 A263257
KEYWORD
nonn,nice
AUTHOR
Christian G. Bower, Dec 19 1999
STATUS
approved