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%I #139 Aug 19 2023 20:51:47
%S 1,2,4,6,10,12,16,19,22,28,32,36,44,49,52,58,65,75,86,94,99,107,116,
%T 128,131,140,149,155,164,176,188,193,206,215,224,237,245,254,268,274,
%U 286,299,307,320,329,342,358,370,380,398,404,416,428,437,453,462,476,488,500,514,528,548,554
%N Maximum gap in one-stage prime-sieves.
%H Thomas R. Hagedorn, <a href="http://dx.doi.org/10.1090/S0025-5718-08-02166-2">Computation of Jacobsthal's function h(n) for n < 50</a>, Math. Comp. 78 (2009) 1073-1087.
%H John F. Morack, <a href="/A072752/a072752_2.txt">Sequences from 1 to 65</a>
%H Mario Ziller and John F. Morack, <a href="https://arxiv.org/abs/1611.03310">Algorithmic concepts for the computation of Jacobsthal's function</a>, arXiv:1611.03310 [math.NT], 2016.
%F For n>=2 we define a(n) = max { m IN N | EXIST c(k) IN N, k=2, .., n : FOR ALL i IN {1, .., m} EXISTS j IN {2, .., n} : i == c(j) (mod prime(j)) }.
%F a(n) = (A048670(n)-2)/2. - _John F. Morack_, Jan 24 2016
%F a(n) = (A058989(n) - 1)/2. - _Mario Ziller_, Dec 08 2016
%e a(5) = 6 because c(2)=2, c(3)=1, c(4)=4, c(5)=3 satisfy the requirements: 1 == 1 (mod 5), 2 == 2 (mod 3), 3 == 3 (mod 11), 4 == 4 (mod 7), 5 == 2 (mod 3), 6 == 1 (mod 5).
%Y Cf. A048670, A058989, A072753.
%K nonn,hard
%O 2,2
%A _Mario Ziller_, Jul 10 2002
%E a(15)-a(16) from _Mario Ziller_, May 30 2005
%E a(17) from _John F. Morack_, Nov 13 2012
%E a(18) from _John F. Morack_, Dec 11 2012
%E a(19) from _Mario Ziller_, Apr 08 2014
%E a(20)-a(21) from _John F. Morack_, Nov 21 2014
%E a(22) from _John F. Morack_, Dec 01 2014
%E a(23) from _John F. Morack_, Dec 05 2014
%E a(24) from _John F. Morack_, Dec 14 2014
%E a(25) from _John F. Morack_, Dec 30 2014
%E a(26)-a(36) from _Mario Ziller_ and _John F. Morack_, May 20 2015
%E a(37)-a(49) from _John F. Morack_ taken from [Hagedorn], Jan 24 2016
%E a(46) corrected and a(50)-a(54) added by _Mario Ziller_, Dec 08 2016
%E a(55)-a(64) from A048670 by _Constantino Calancha_, Aug 05 2023
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