A247970 - OEIS

%I #8 Jan 27 2015 15:46:56

%S 3,3,3,3,3,3,3,24,24,140,140,140,140,140,140,140,140,140,140,140,140

%N a(n) is the smallest k such that prime(k+i) (mod 6) takes successively the values 5,1,5,1... for i = 0, 1,...,n-1 ending with 1 or 5.

%C If a(22) exists, k > 10^5.

%e a(1)= 3 => prime(3) (mod 6)= 5;

%e a(2)= 3 => prime(3) (mod 6)= 5, prime(4) (mod 6) = 1;

%e a(3)= 3 => prime(3) (mod 6)= 5, prime(4) (mod 6)= 1, prime(5) (mod 6)= 5.

%p with(numtheory):

%p for n from 1 to 35 do :

%p ii:=0:

%p    for k from 3 to 10^5 while (ii=0)do :

%p      s:=0:

%p       for i from 0 to n-1 do:

%p         r:=irem(ithprime(k+i),6):

%p         if r = irem(5^(i+1),6)

%p         then

%p         s:=s+1:

%p         else

%p         fi:

%p       od:

%p        if s=n and ii=0

%p        then

%p        printf ( "%d %d \n",n,k):ii:=1:

%p        else

%p        fi:

%p     od:

%p od:

%Y Cf. A039704, A247816, A247967, A247969.

%K nonn,more

%O 1,1

%A _Michel Lagneau_, Sep 28 2014