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

Fran├žois Marques, Dec 07 2020

STATUS

approved

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Last modified June 19 12:45 EDT 2021. Contains 345129 sequences. (Running on oeis4.)