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%I #67 Sep 26 2021 14:17:04
%S 1,1,1,4,1,1,2,1,1,2,1,2,4,1,1,2,2,1,10,1,1,6,1,2,6,1,2,136,1,1,6,6,1,
%T 6,1,1,2,2,1,2,1,2,4,1,2,4,4,1,2,1,1,44,1,1,2,1,3,2,5,3,2,2,1,4,1,768,
%U 4,1,1,52,34,2,132,1,1,14,7,1,2,2,1,8,1,2,10,1,24,60,1,1,2,3,5,2,1,1,2,1,1
%N Least k such that 2*n^k - 1 is prime.
%C From _Eric Chen_, Jun 01 2015: (Start)
%C Conjecture: a(n) is defined for all n.
%C a(303) > 10000, a(304)..a(360) = {1, 2, 11, 1, 990, 1, 1, 2, 2, 4, 74, 5, 1, 10, 6, 6, 4, 1, 1, 2, 1, 9, 12, 1, 80, 2, 1, 1, 2, 14, 3, 2, 3, 1, 12, 1, 60, 36, 1, 8, 4, 34, 1, 522, 3, 15, 14, 1, 6, 2, 3, 1, 4, 5, 4, 10, 1}.
%C a(n) = 1 if and only if n is in A006254. (End)
%C From _Eric Chen_, Sep 16 2021: (Start)
%C Now a(303) is known to be 40174, also other terms > 10000: a(383) = 20956, a(515) = 58466, a(522) = 62288, a(578) = 129468, a(581) > 400000, a(590) = 15526, a(647) = 21576, a(662) = 16590, a(698) = 127558, a(704) = 62034, see the a-file and the references.
%C a(n) = 2 if and only if n is in A066049 but not in A006254.
%C a(n) = 3 if and only if n is in A214289 but not in A006254 or A066049. (End)
%H Eric Chen, <a href="/A119591/b119591.txt">Table of n, a(n) for n = 2..580</a>
%H Gary Barnes, <a href="http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm">Riesel conjectures and proofs</a>
%H Eric Chen, <a href="/A119591/a119591_1.txt">Table of n, a(n) for n = 2..2050 status</a>
%H Prime Wiki, <a href="https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n">Riesel prime small bases least n</a>
%F From _Eric Chen_, Sep 16 2021: (Start)
%F a(6*n) = A098873(n).
%F a(2^n) = A279095(n).
%F a(A006254(n)) = 1.
%F a(A066049(n)) <= 2.
%F a(A214289(n)) <= 3. (End)
%t f[n_] := Block[{k = 0}, While[ ! PrimeQ[2*n^k - 1], k++ ]; k ]; Table[f[n], {n, 2, 106}] (* _Ray Chandler_, Jun 08 2006 *)
%o (PARI) a(n) = for(k=1, 2^24, if(ispseudoprime(2*n^k-1), return(k))) \\ _Eric Chen_, Jun 01 2015
%Y Cf. A119624, A253178.
%Y Numbers r such that 2*k^r-1 is prime: A090748 (k=2), A003307 (k=3), A146768 (k=4), A120375 (k=5), A057472 (k=6), A002959 (k=7), ... (k=8), ... (k=9), A002957 (k=10), A120378 (k=11), ... (k=12), A174153 (k=13), A273517 (k=14), ... (k=15), ... (k=16), A193177 (k=17), A002958 (k=25).
%K nonn,hard
%O 2,4
%A _Pierre CAMI_, Jun 01 2006
%E Corrected and extended by _Ray Chandler_, Jun 08 2006
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