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.

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

Author

Christian G. Bower, Dec 19 1999

Keywords

• nonn
• nice

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]

Examples

			a(4)=19 because 4 -> 9 (composite) -> 19 (prime).
		

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]

Crossrefs

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

Cf. A051914, A052334, A052339, A052340, A040081.

Programs

Mathematica

Table[NestWhile[2#+1&,2n+1,!PrimeQ[#]&,1,1000],{n,60}] (* Harvey P. Dale, May 08 2011 *)

PARI

a(n)=while(!isprime(n=2*n+1),);n \\ oo loop when a(n) = 0. - Charles R Greathouse IV, May 08 2011