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A108129
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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.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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Hans Riesel, Några stora primtal, Elementa 39 (1956), pp. 258-260.
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LINKS
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MATHEMATICA
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Array[Function[k, SelectFirst[Range@300, PrimeQ[k 2^# - 1] &]][2 # - 1] &, 102] (* Michael De Vlieger, Jan 12 2018 *)
smk[n_]:=Module[{m=1, k=2n-1}, While[!PrimeQ[k 2^m-1], m++]; m]; Array[smk, 120] (* Harvey P. Dale, Dec 26 2023 *)
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PROG
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(PARI) forstep(k=1, 301, 2, n=1; while(!isprime(k*2^n-1), n++); print1(n, ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 25 2006
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STATUS
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approved
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