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, 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

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*(np-p)), 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