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A214450 Smallest prime p such that n primes exist between the prime triple (p, p+2, p+6) and the next prime triple.

%I A214450 #8 Feb 21 2023 09:59:43
%S A214450 5,857,311,17,31391,3461,1427,12917,1997,4517,41,20747,107,1871,1487,
%T A214450 4637,2081,347,7877,23057,80777,1091,18041,641,461,5231,21017,881,
%U A214450 4967,45821,1607,15731,165311,17027,35591,26261,11777,8537,64151,101111,82757,23741
%N A214450 Smallest prime p such that n primes exist between the prime triple (p, p+2, p+6) and the next prime triple.
%e A214450 a(3)= 17 because there exists 3 primes 29, 31 and 37 are between (17, 19,23) and (41,43,47).
%p A214450 A214450 := proc(n)
%p A214450 local j, hi, lo ;
%p A214450 if n = 0 then
%p A214450 3;
%p A214450 else
%p A214450 for j from 1 do
%p A214450 hi := numtheory[pi]( A022004 (j+1)) ;
%p A214450 lo := numtheory[pi]( A098412 (j)) ;
%p A214450 if hi-lo = n+1 then
%p A214450 return A022004 (j);
%p A214450 end if;
%p A214450 end do:
%p A214450 end if;
%p A214450 end proc: # [Program from R. J. Mathar, adapted for this sequence (see A089637)].
%Y A214450 Cf. A022004, A098412, A089637.
%K A214450 nonn
%O A214450 0,1
%A A214450 _Michel Lagneau_, Jul 18 2012