Voozh

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

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

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, n-1,

if(gcd(a, n)>1, todo=bitnegimply(todo, 1<<a))

);

todo=bitnegimply(todo, 1<<2);

forprime(p=3, default(primelimit),

r+=p-q;

r=r%n;

todo=bitnegimply(todo, 1<<r);