|
| |
|
|
A108129
|
|
Riesel problem: let k=2n-1; then a(n)=smallest m >= 1 such that k*2^m-1 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^m-1 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, Några stora primtal, Elementa 39 (1956), pp. 258-260.
|
|
|
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. 259-264. (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 n-phi(n), Colloq. Math., 68 (1995), pp. 55-58.
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^n-1), 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
|
| |
|
|
