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A247970 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.

%I A247970 #8 Jan 27 2015 15:46:56
%S A247970 3,3,3,3,3,3,3,24,24,140,140,140,140,140,140,140,140,140,140,140,140
%N A247970 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 A247970 If a(22) exists, k > 10^5.
%e A247970 a(1)= 3 => prime(3) (mod 6)= 5;
%e A247970 a(2)= 3 => prime(3) (mod 6)= 5, prime(4) (mod 6) = 1;
%e A247970 a(3)= 3 => prime(3) (mod 6)= 5, prime(4) (mod 6)= 1, prime(5) (mod 6)= 5.
%p A247970 with(numtheory):
%p A247970 for n from 1 to 35 do :
%p A247970 ii:=0:
%p A247970    for k from 3 to 10^5 while (ii=0)do :
%p A247970      s:=0:
%p A247970       for i from 0 to n-1 do:
%p A247970         r:=irem(ithprime(k+i),6):
%p A247970         if r = irem(5^(i+1),6)
%p A247970         then
%p A247970         s:=s+1:
%p A247970         else
%p A247970         fi:
%p A247970       od:
%p A247970        if s=n and ii=0
%p A247970        then
%p A247970        printf ( "%d %d \n",n,k):ii:=1:
%p A247970        else
%p A247970        fi:
%p A247970     od:
%p A247970 od:
%Y A247970 Cf. A039704, A247816, A247967, A247969.
%K A247970 nonn,more
%O A247970 1,1
%A A247970 _Michel Lagneau_, Sep 28 2014