A204894 - OEIS

%I #17 Aug 31 2024 14:29:55

%S 3,5,5,7,7,11,17,11,11,13,13,17,29,17,17,19,19,23,41,23,23,29,53,29,

%T 53,29,29,31,31,37,67,37,71,37,37,41,79,41,41,43,43,47,89,47,47,53,97,

%U 53,101,53,53,59,109,59,113,59,59,61,61,67,127,67,131,67,67,71

%N Least prime p such that n divides p-q for some prime q<p.

%C For a guide to related sequences, see A204892.

%H Charles R Greathouse IV, <a href="/A204894/b204894.txt">Table of n, a(n) for n = 1..10000</a>

%H Tony Haddad, Sun-Kai Leung, and Cihan Sabuncu, <a href="https://arxiv.org/abs/2408.11781">Visiting early at prime times</a>, arXiv preprint (2024). arXiv:2408.11781 [math.NT]

%F n + 2 <= a(n) <= prime(n+1). - _Charles R Greathouse IV_, Jul 17 2015

%F Haddad, Leung, & Sabuncu prove that a(n) < 270*n for all large n. Probably this holds for all n. - _Charles R Greathouse IV_, Aug 29 2024

%t (See the program at A204892.)

%o (PARI) a(n)=forprime(p=n+2, , forstep(k=p%n, p-1, n, if(isprime(k), return(p)))) \\ _Charles R Greathouse IV_, Mar 20 2013

%o (PARI) a(n)=if(isprime(n+2),return(n+2)); my(s=if(n%2,2*n,n),t); forprime(p=s+3,, t=p%n; forstep(q=if(t%2,t,t+n),p-s,s,if(isprime(q), return(p)))) \\ _Charles R Greathouse IV_, Jul 17 2015

%o (PARI) a(n)=if(isprime(n+2),return(n+2)); my(s=if(n%2,2*n,n),r); forprime(p=s+3,2*s+1, if(isprime(p-s), return(p))); forprime(p=2*s+3,, r=p%n; forstep(q=if(r%2,r,r+n),p-s,s,if(isprime(q), return(p)))) \\ _Charles R Greathouse IV_, Aug 31 2024

%Y Cf. A204892, A204903, A000040.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 20 2012