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

1,1

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);
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, n-1, 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