A072752 Maximum gap in one-stage prime-sieves.
1, 2, 4, 6, 10, 12, 16, 19, 22, 28, 32, 36, 44, 49, 52, 58, 65, 75, 86, 94, 99, 107, 116, 128, 131, 140, 149, 155, 164, 176, 188, 193, 206, 215, 224, 237, 245, 254, 268, 274, 286, 299, 307, 320, 329, 342, 358, 370, 380, 398, 404, 416, 428, 437, 453, 462, 476, 488, 500, 514, 528, 548, 554
Offset: 2
Examples
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).
Links
- Thomas R. Hagedorn, Computation of Jacobsthal's function h(n) for n < 50, Math. Comp. 78 (2009) 1073-1087.
- John F. Morack, Sequences from 1 to 65
- Mario Ziller and John F. Morack, Algorithmic concepts for the computation of Jacobsthal's function, arXiv:1611.03310 [math.NT], 2016.
Formula
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)) }.
a(n) = (A048670(n)-2)/2. - John F. Morack, Jan 24 2016
a(n) = (A058989(n) - 1)/2. - Mario Ziller, Dec 08 2016
Extensions
a(15)-a(16) from Mario Ziller, May 30 2005
a(17) from John F. Morack, Nov 13 2012
a(18) from John F. Morack, Dec 11 2012
a(19) from Mario Ziller, Apr 08 2014
a(20)-a(21) from John F. Morack, Nov 21 2014
a(22) from John F. Morack, Dec 01 2014
a(23) from John F. Morack, Dec 05 2014
a(24) from John F. Morack, Dec 14 2014
a(25) from John F. Morack, Dec 30 2014
a(26)-a(36) from Mario Ziller and John F. Morack, May 20 2015
a(37)-a(49) from John F. Morack taken from [Hagedorn], Jan 24 2016
a(46) corrected and a(50)-a(54) added by Mario Ziller, Dec 08 2016
a(55)-a(64) from A048670 by Constantino Calancha, Aug 05 2023