

A088444


Smallest divisor d of n such that all intervals [(k1)*d+1:k*d] contain at least one prime, 1<=k<=n/d; a(1)=1.


7



1, 2, 3, 2, 5, 2, 7, 2, 3, 5, 11, 3, 13, 7, 3, 4, 17, 3, 19, 4, 3, 11, 23, 3, 5, 13, 9, 7, 29, 5, 31, 8, 11, 17, 5, 6, 37, 19, 13, 5, 41, 6, 43, 11, 5, 23, 47, 6, 7, 5, 17, 13, 53, 6, 5, 7, 19, 29, 59, 5, 61, 31, 7, 8, 5, 6, 67, 17, 23, 5, 71, 6, 73, 37, 5, 19, 7, 6, 79, 5, 9, 41, 83, 6
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OFFSET

1,2


COMMENTS

A088445(n) = n / a(n);
a(n)=n iff n=1 or n is prime: a(A008578(n))=A008578(n), a(A002808(n)) < A002808(n); A088447(a(n)) <= n <= A088448(a(n)).


LINKS

Table of n, a(n) for n=1..84.
Eric Weisstein's World of Mathematics, Prime Gaps


EXAMPLE

n=30: a(30)>3 as [25:27] = {25,26,27} contains no prime, but
a(30)=5 as 3 in [1:5], 7 in [6:10], 11 in [11:15], 17 in [16:20], 23 in
[21:25], 29 in [26:30].


CROSSREFS

Cf. A088449, A088450, A088451.
Sequence in context: A086765 A079868 A280697 * A108077 A248737 A141310
Adjacent sequences: A088441 A088442 A088443 * A088445 A088446 A088447


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Sep 30 2003


STATUS

approved



