cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A214925 Number of primes <= A214757(n).

Original entry on oeis.org

5, 5, 5, 10, 25, 31, 104, 159, 190, 219, 1186, 1832, 2227, 3388, 14358, 30804, 31547, 40935, 103522, 104072, 149690, 325853, 1094426, 1319950, 2850175, 6957880, 10539433, 10655464
Offset: 1

Views

Author

John W. Nicholson, Aug 06 2012

Keywords

Examples

			A214757(4) = 29, so a(4) = primepi(A214757(4)) = primepi(29) = 10.

Crossrefs

Cf. A000101, A104272, A214756, A001223.
Cf. A002386, A214924, A214926, A214757.

Formula

a(n) = pi(A214757(n)) = A000217(A214757(n)).

Extensions

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

A214756 a(n) = largest Ramanujan prime R_k in A104272 that is <= A002386(n).

Original entry on oeis.org

2, 2, 2, 17, 71, 107, 503, 881, 1103, 1301, 9521, 15671, 19543, 31387, 155849, 360289, 370061, 492067, 1349147, 1356869, 2010553, 4652239, 17051297, 20831119, 47326519, 122164649, 189695483, 191912659
Offset: 1

Views

Author

John W. Nicholson, Jul 27 2012

Keywords

Comments

While many values in A214757(n) are equal to A000101(n), here it seems the only value such that A002386(n) is equal to a(n) is a(1) = R_k = A002386(1) = 2.
See "Let rho(m) = A179196(m)" comment at A001223.

Examples

			A104272(94) = 1301 < 1327 = A002386(10), so a(10) = 1301.

Links

Crossrefs

Cf. A002386, A104272, A001223.
Cf. A214925, A214926, A214757, A214924.

Programs

  • Perl
    use ntheory ":all";  sub a_from_2386 { my $n = shift; $n = prev_prime($n) while !is_ramanujan_prime($n); $n } # Dana Jacobsen, Jul 13 2016
  • Perl
    perl -Mntheory=:all -nE 'my $n=$1 if /(\d+)$/; $r=ramanujan_primes($n>1e6 ? $n-1e6 : 2, $n); say ++$x," ",$r->[-1];' b002386.txt # Dana Jacobsen, Jul 13 2016

Extensions

Edited by N. J. A. Sloane, Aug 06 2012
a(16)-a(28) from Donovan Johnson, Nov 04 2012

A214924 Number of primes <= A214756(n).

Original entry on oeis.org

1, 1, 1, 7, 20, 28, 96, 152, 185, 212, 1179, 1829, 2217, 3382, 14350, 30780, 31528, 40929, 103498, 104047, 149674, 325845, 1094396, 1319933, 2850163, 6957867, 10539421, 10655453
Offset: 1

Views

Author

John W. Nicholson, Jul 29 2012

Keywords

Comments

a(n) = pi(A214756(n)).

Examples

			A214756(5) = 71, so a(5) = primepi(A214756(5)) = primepi(71) = 20.

Crossrefs

Cf. A000101, A104272, A214756, A001223.
Cf. A002386, A214925, A214926, A214757.

Formula

a(n) = A000217(A214756(n))

Extensions

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

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

Original entry on oeis.org

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

Views

Author

John W. Nicholson, Aug 06 2012

Keywords

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

Examples

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

Crossrefs

Cf. A214924, A214925, A214756, A214757.
Cf. A000101, A104272, A001223, A002386.

Formula

a(n) = pi(A214757(n)) - pi(A214756(n)).
a(n) = rho(A214757(n)) - rho(A214756(n)).

Extensions

Extension to a(28) added by John W. Nicholson, Nov 11 2013
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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