

A108129


Riesel problem: let k=2n1; then a(n)=smallest m >= 1 such that k*2^m1 is prime, or 1 if no such prime exists.


3



2, 1, 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, 1, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

It is conjectured that the integer k = 509203 is the smallest Riesel number, that is, the first n such that a(n) = 1 is 254602.
Browkin & Schinzel, having proved that 509203*2^k  1 is composite for all k > 0, ask for the first such number with this property, noting that the question is implicit in Aigner 1961.  Charles R Greathouse IV, Jan 12 2018
Record values begin a(1) = 2, a(7) = 3, a(12) = 4, a(22) = 7, a(30) = 12, a(64) = 25, a(96) = 226, a(330) = 800516; the next record appears to be a(1147), unless a(1147) = 1. (The value for a(330), i.e., for k = 659, is from the Ballinger & Keller link, which also lists k = 2293, i.e., n = (k+1)/2 = (2293+1)/2 = 1147, as the smallest of 50 values of k < 509203 for which no prime of the form k*2^m1 had yet been found.)  Jon E. Schoenfield, Jan 13 2018
Same as A046069 except for a(2) = 1.  Georg Fischer, Nov 03 2018


REFERENCES

Hans Riesel, NĂ¥gra stora primtal, Elementa 39 (1956), pp. 258260.


LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..329
A. Aigner, Folgen der Art ar^n + b, welche nur teilbare Zahlen liefern, Math. Nachr. 23 (1961), pp. 259264. (Cited in Browkin & Schinzel)
R. Ballinger & W. Keller, The Riesel Problem: Definition and Status.
J. Browkin and A. Schinzel, On integers not of the form nphi(n), Colloq. Math., 68 (1995), pp. 5558.
Wilfrid Keller, List of primes k.2^n  1 for k < 300 .


MATHEMATICA

Array[Function[k, SelectFirst[Range@300, PrimeQ[k 2^#  1] &]][2 #  1] &, 102] (* Michael De Vlieger, Jan 12 2018 *)


PROG

(PARI) forstep(k=1, 301, 2, n=1; while(!isprime(k*2^n1), n++); print1(n, ", "))


CROSSREFS

Cf. A040081, A046069.
Sequence in context: A298485 A332997 A298614 * A078349 A266476 A081327
Adjacent sequences: A108126 A108127 A108128 * A108130 A108131 A108132


KEYWORD

nonn


AUTHOR

Jorge Coveiro, Jun 04 2005


EXTENSIONS

Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 25 2006
Name corrected by T. D. Noe, Feb 13 2011


STATUS

approved



