A339501 a(n) = smallest prime number between prime(n) and 2*prime(n) such that the arithmetic progression (prime(n), a(n), ...) and which contains only primes has the maximum length.

3, 5, 7, 13, 17, 17, 29, 31, 41, 41, 37, 67, 47, 61, 59, 71, 83, 67, 97, 131, 127, 103, 131, 101, 139, 197, 193, 137, 151, 173, 139, 191, 167, 151, 233, 181, 307, 271, 197, 233, 263, 211, 317, 283, 359, 211, 241, 373, 239, 271, 311, 359, 277

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

a(4) = 13 since 7, 13 and 19 are primes in arithmetic progression, 7 is the fourth prime number, and there is no longer one starting with 7 than another prime less than 2*7 = 14.
a(12) = 67 since prime(12) = 37 and 67, 97, 127 and 157 are also primes in arithmetic progression of common difference 30.

Prog

(PARI) A339501(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(bp);
}

Crossrefs

Cf. A000040, A339500.

Sequence in context: A188574 A247458 A355424 * A008996 A261089 A264988

Adjacent sequences: A339498 A339499 A339500 * A339502 A339503 A339504

Keyword

nonn,easy

Author

François Marques, Dec 07 2020

Status

approved