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A214926
Difference A214925(n) - A214924(n), prime count between Ramanujan primes bounding maximal gap primes.
4
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
OFFSET
1,1
COMMENTS
Conjecture: For every n > 0, a(n) > 1.
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
FORMULA
a(n) = pi(A214757(n)) - pi(A214756(n)).
a(n) = rho(A214757(n)) - rho(A214756(n)).
EXAMPLE
a(4) = pi(A214757(4)) - pi(A214756(4)) = 10 - 7 = 3
KEYWORD
nonn
AUTHOR
John W. Nicholson, Aug 06 2012
EXTENSIONS
Extension to a(28) added by John W. Nicholson, Nov 11 2013
STATUS
approved