A214926 Difference A214925(n) - A214924(n), prime count between Ramanujan primes bounding maximal gap primes.

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

Links

Table of n, a(n) for n=1..28.

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

Crossrefs

Cf. A214924, A214925, A214756, A214757.

Cf. A000101, A104272, A001223, A002386.

Sequence in context: A023977 A073259 A174987 * A268368 A274947 A331961

Adjacent sequences: A214923 A214924 A214925 * A214927 A214928 A214929

Keyword

nonn

Author

John W. Nicholson, Aug 06 2012

Extensions

Extension to a(28) added by John W. Nicholson, Nov 11 2013

Status

approved