

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


COMMENTS

This sequence seems to generate lots of primes if you add 1 to each term: 2, 3, 5, 7, 11, 13, 17, 20, 23, 29, 33, 37, 45, 50, 53, 59, 66.  John F. Morack, Nov 14 2012


LINKS

Table of n, a(n) for n=2..24.
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
John F. Morack, A partial set of sequences of length 116


FORMULA

Let prime(n) be the sequence of primes, i.e. 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)) }


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: A127965 A117891 A178539 * A036634 A005942 A024907
Adjacent sequences: A072749 A072750 A072751 * A072753 A072754 A072755


KEYWORD

hard,more,nonn,changed


AUTHOR

Mario Ziller, Jul 10 2002


EXTENSIONS

2 more terms from Mario Ziller, May 30 2005
1 more term from John F. Morack, Nov 13 2012
1 more term 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


STATUS

approved



