

A339500


Maximum length of sequences of prime numbers that start with prime(n) and are arithmetic progressions of common difference less than prime(n).


2



2, 3, 2, 3, 4, 2, 4, 3, 3, 3, 3, 5, 4, 4, 4, 4, 4, 4, 4, 5, 3, 4, 4, 3, 4, 4, 5, 6, 3, 5, 4, 4, 5, 3, 4, 5, 6, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 5, 4, 3, 4, 6, 4, 4, 6, 5, 4, 4, 5, 6, 4, 4, 5, 4, 4, 4, 6, 4, 4, 4, 5, 6, 5, 4, 5, 5, 6, 6, 5, 9, 5, 4
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..82.


EXAMPLE

a(4) = 3 since 7 is the fourth prime number and 7, 13 and 19 are primes in arithmetic progression of common difference equal to 6 and there is no longer arithmetic sequence starting with 7 of common difference < 7 which contains only prime numbers.
a(12) = 5 since prime(12) = 37 and 67, 97, 127 and 157 are also primes in arithmetic progression of common difference 30 < 37.


PROG

(PARI) A339500(n)= {
my(p=prime(n), bp, bk);
forprime(np=p+1, 2*p, for(k=2, +oo, if(!isprime(p+k*(npp)), if(k>bk, bk=k; bp=np; ); break); ); );
return(bk);
}


CROSSREFS

Cf. A000040, A339501.
Sequence in context: A130799 A243519 A278102 * A106383 A175794 A324389
Adjacent sequences: A339497 A339498 A339499 * A339501 A339502 A339503


KEYWORD

nonn,easy


AUTHOR

François Marques, Dec 07 2020


STATUS

approved



