A038026 Last position reached by winner of n-th Littlewood Frog Race.

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

Offset: 1

Author

Christian G. Bower

Keywords

• nonn

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

Examples

			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
		

Links

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

Crossrefs

This sequence is a lower bound for the related sequence A085420.

Cf. A038025.

Programs

PARI

a(n)={
my(todo=(1<1,todo=bitnegimply(todo,1<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,n-1,if(gcd(n,b)==1,t=max(t,p(n,b))));t \\ Charles R Greathouse IV, Sep 08 2012

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