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

2,2

Links

Table of n, a(n) for n=2..64.

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

Example

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).

Crossrefs

Cf. A048670, A058989, A072753.

Sequence in context: A117891 A262935 A178539 * A036634 A005942 A024907

Adjacent sequences: A072749 A072750 A072751 * A072753 A072754 A072755

Keyword

nonn,hard

Author

Mario Ziller, Jul 10 2002

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

Status

approved