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Difference A214925(n) - A214924(n), prime count between Ramanujan primes bounding maximal gap primes.
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%I #26 Nov 19 2013 13:58:23

%S 4,4,4,3,5,3,8,7,5,7,7,3,10,6,8,24,19,6,24,25,16,8,30,17,12,13,12,11

%N Difference A214925(n) - A214924(n), prime count between Ramanujan primes bounding maximal gap primes.

%C Conjecture: For every n > 0, a(n) > 1.

%C Let rho(m) = A179196(m), for any n, let m be an integer such that p_(rho(m)) <= p_n and p_(n+1) <= p_(rho(m+1)), then rho(m) <= n < n + 1 <= rho(m + 1), therefore A001223(n) = p_(n+1) - p_n <= p_rho(m+1) - p_rho(m) = A182873(m). For all rho(m) = A179196(m), A001223(rho(m)) < A165959(m). (Comment copied from A001223). _John W. Nicholson_, Nov 17 2013

%F a(n) = pi(A214757(n)) - pi(A214756(n)).

%F a(n) = rho(A214757(n)) - rho(A214756(n)).

%e a(4) = pi(A214757(4)) - pi(A214756(4)) = 10 - 7 = 3

%Y Cf. A214924, A214925, A214756, A214757.

%Y Cf. A000101, A104272, A001223, A002386.

%K nonn

%O 1,1

%A _John W. Nicholson_, Aug 06 2012

%E Extension to a(28) added by _John W. Nicholson_, Nov 11 2013