

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
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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..19.
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


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


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


STATUS

approved



