A339500 - OEIS

%I #23 Dec 26 2020 21:12:04

%S 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,

%T 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,

%U 4,4,5,6,5,4,5,5,6,6,5,9,5,4

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

%e 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.

%e a(12) = 5 since prime(12) = 37 and 67, 97, 127 and 157 are also primes in arithmetic progression of common difference 30 < 37.

%o (PARI) A339500(n)= {

%o   my(p=prime(n), bp, bk);

%o   forprime(np=p+1, 2*p, for(k=2, +oo, if(!isprime(p+k*(np-p)), if(k>bk, bk=k; bp=np;); break); ); );

%o   return(bk);

%o }

%Y Cf. A000040, A339501.

%K nonn,easy

%O 1,1

%A _François Marques_, Dec 07 2020