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 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

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Last modified September 26 16:06 EDT 2021. Contains 347668 sequences. (Running on oeis4.)