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A038026 Last position reached by winner of n-th Littlewood Frog Race. 6
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. [From 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: A228775 A129543 A137440 * A051860 A155766 A153488

Adjacent sequences:  A038023 A038024 A038025 * A038027 A038028 A038029

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified June 29 01:52 EDT 2017. Contains 288857 sequences.