

A038026


Last position reached by winner of nth Littlewood Frog Race.


8



2, 3, 7, 5, 19, 7, 29, 17, 19, 19, 43, 13, 103, 29, 31, 41, 103, 19, 191, 41, 67, 43, 137, 73, 149, 103, 109, 83, 317, 31, 311, 97, 181, 103, 191, 71, 439, 191, 233, 89, 379, 67, 463, 113, 181, 137, 967, 97, 613, 149, 197, 181, 607, 109, 331, 233
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OFFSET

1,1


COMMENTS

Related to Linnik's theorem; main sequence is A085420.  Charles R Greathouse IV, Apr 16 2010
a(n) is the smallest prime such that some subset of primes <= a(n) is a reduced residue system modulo n.  Vladimir Shevelev, Feb 19 2013


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

Let p(n,b) be the smallest prime in the arithmetic progression k*n+b, with k >= 0. Then a(n) = max(p(n,b)) with 0 < b < n and gcd(b,n) = 1.  Charles R Greathouse IV, Sep 08 2012


EXAMPLE

a(6) = 7 since the primes less than or equal to 7, {2, 3, 5, 7}, reduced modulo 6 are {2, 3, 5, 1}. This contains the reduced residue system modulo 6, which is {1, 5}, and 7 is clearly the smallest such prime.  Vladimir Shevelev, Feb 19 2013


PROG

(PARI) a(n)={
my(todo=(1<<n)1, r=2, q=2);
if(n==1, return(2));
for(a=0, n1,
if(gcd(a, n)>1, todo=bitnegimply(todo, 1<<a))
);
todo=bitnegimply(todo, 1<<2);
forprime(p=3, default(primelimit),
r+=pq;
r=r%n;
todo=bitnegimply(todo, 1<<r);
if(!todo, return(p));
q=p;
);
error("Not enough precomputed primes")
}; \\ Charles R Greathouse IV, Feb 14 2011
(PARI) p(n, b)=while(!isprime(b), b+= n); b
a(n)=my(t=p(n, 1)); for(b=2, n1, if(gcd(n, b)==1, t=max(t, p(n, b)))); t \\ Charles R Greathouse IV, Sep 08 2012


CROSSREFS

This sequence is a lower bound for the related sequence A085420.
Cf. A038025.
Sequence in context: A129543 A137440 A294639 * A051860 A351494 A155766
Adjacent sequences: A038023 A038024 A038025 * A038027 A038028 A038029


KEYWORD

nonn


AUTHOR

Christian G. Bower


STATUS

approved



