

A072752


Maximum gap in onestage primesieves.


3



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
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OFFSET

2,2


COMMENTS

All values in this sequence can be directly calculated from A048670 by replacing each term T by (T2)/2. Terms from a(37) to a(49) are from T. R. Hagedorn's article.John F. Morack, Jan 24 2016


LINKS

Table of n, a(n) for n=2..54.
Thomas R. Hagedorn, Computation of Jacobsthal's function h(n) for n < 50, Math. Comp. 78 (2009) 10731087.
John F. Morack, Sequences from 1 to 65
John F. Morack, Exhaustive table of distributions of holes in sequences primes 3 to 31 over a range of consecutive numbers of length 65 to 79 [Title needs editing!  N. J. A. Sloane, Feb 28 2016]
John F. Morack, A partial set of sequences of length 116
Mario Ziller, John F. Morack, Algorithmic concepts for the computation of Jacobsthal's function, arXiv:1611.03310 [math.NT], 2016.


FORMULA

Let {prime(n): n >= 1} denote the sequence of primes, e.g. prime(1)=2. 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 = (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. A072753.
Sequence in context: A117891 A262935 A178539 * A036634 A005942 A024907
Adjacent sequences: A072749 A072750 A072751 * A072753 A072754 A072755


KEYWORD

hard,more,nonn,changed


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, Jan 24 2016
a(46) corrected and a(50)a(54) added by Mario Ziller, Dec 08 2016


STATUS

approved



