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 1-6 of 6 results.

A059111 a(n) = floor(prime(n) - n*log(n)).

Original entry on oeis.org

2, 1, 1, 1, 2, 2, 3, 2, 3, 5, 4, 7, 7, 6, 6, 8, 10, 8, 11, 11, 9, 10, 10, 12, 16, 16, 14, 13, 11, 10, 20, 20, 21, 19, 24, 21, 23, 24, 24, 25, 26, 24, 29, 26, 25, 22, 30, 37, 36, 33, 32, 33, 30, 35, 36, 37, 38, 35, 36, 35, 32, 37, 45, 44, 41, 40, 49, 50, 54, 51, 50, 51, 53, 54, 55
Offset: 1

Views

Author

Henry Bottomley, Jan 04 2001

Keywords

Links

Crossrefs

Cf. A064658, A064659, A059112.

Programs

  • Magma
    [ Floor(NthPrime(n)-n*Log(n)): n in [1..75] ];  // Bruno Berselli, May 02 2011
  • Mathematica
    Table[Floor[Prime[n]-n Log[n]],{n,100}] (* Harvey P. Dale, May 02 2011 *)
  • PARI
    { default(realprecision, 100); for (n = 1, 1000, write("b059111.txt", n, " ", floor(prime(n) - n*log(n))); ) } \\ Harry J. Smith, Jun 25 2009

Extensions

Definition corrected by Harry J. Smith, Jun 24 2009

A064658 a(n) = ceiling(prime(n) - n*log(n)).

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 4, 3, 4, 6, 5, 8, 8, 7, 7, 9, 11, 9, 12, 12, 10, 11, 11, 13, 17, 17, 15, 14, 12, 11, 21, 21, 22, 20, 25, 22, 24, 25, 25, 26, 27, 25, 30, 27, 26, 23, 31, 38, 37, 34, 33, 34, 31, 36, 37, 38, 39, 36, 37, 36, 33, 38, 46, 45, 42, 41, 50, 51, 55
Offset: 1

Views

Author

N. J. A. Sloane, Oct 10 2001

Keywords

Links

Crossrefs

Cf. A064659, A059111.

Programs

  • Mathematica
    Table[Ceiling[Prime[n]-n Log[n]],{n,70}] (* Harvey P. Dale, Dec 07 2018 *)
  • PARI
    { default(realprecision, 100); for (n = 1, 1000, write("b064658.txt", n, " ", ceil(prime(n) - n*log(n))); ) } \\ Harry J. Smith, Jun 25 2009

Formula

a(n) ~ n*log(log(n)) * (1 + 1/log(n) - 1/log(log(n)) - 2/(log(n)*log(log(n)))). - Vaclav Kotesovec, May 23 2020

Extensions

Definition corrected by Harry J. Smith, Jun 24 2009

A064663 a(n) = n - ceiling( prime(n)/log(prime(n)) ).

Original entry on oeis.org

-2, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 5, 5, 6, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 6, 7, 7, 8, 7, 6, 7, 7, 8, 8, 9, 8, 8, 8, 8, 9, 9, 10, 10, 10, 9, 9, 10, 10, 9, 10, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 11, 11, 12, 11
Offset: 1

Views

Author

N. J. A. Sloane, Oct 10 2001

Keywords

Links

Crossrefs

Cf. A064659-A064662.

Programs

  • Mathematica
    Table[n-Ceiling[Prime[n]/Log[Prime[n]]],{n,90}] (* Harvey P. Dale, Dec 05 2012 *)
  • PARI
    { for (n=1, 1000, write("b064663.txt", n, " ", n - ceil( prime(n)/log(prime(n)) )) ) } \\ Harry J. Smith, Sep 21 2009

A064662 a(n) = n - round( prime(n)/log(prime(n)) ).

Original entry on oeis.org

-2, -1, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 11, 10, 9, 10, 11, 11, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12
Offset: 1

Views

Author

N. J. A. Sloane, Oct 10 2001

Keywords

Links

Crossrefs

Cf. A064659-A064663.

Programs

  • Magma
    [n - Round(NthPrime(n) / Log(NthPrime(n))): n in [1..100]]; // Vincenzo Librandi, May 25 2019
  • Mathematica
    rpl[n_]:=Module[{p=Prime[n]},n-Round[p/Log[p]]]; Array[rpl,90] (* Harvey P. Dale, May 20 2019 *)
  • PARI
    { for (n=1, 1000, write("b064662.txt", n, " ", n - round( prime(n)/log(prime(n)) )) ) } \\ Harry J. Smith, Sep 21 2009

A064661 a(n) = n - floor( prime(n)/log(prime(n)) ).

Original entry on oeis.org

-1, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 4, 5, 5, 6, 6, 7, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 7, 8, 8, 9, 8, 7, 8, 8, 9, 9, 10, 9, 9, 9, 9, 10, 10, 11, 11, 11, 10, 10, 11, 11, 10, 11, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 12, 12
Offset: 1

Views

Author

N. J. A. Sloane, Oct 10 2001

Keywords

Links

Crossrefs

Cf. A064659-A064663.

Programs

  • Mathematica
    Table[n-Floor[Prime[n]/Log[Prime[n]]],{n,90}] (* Harvey P. Dale, Sep 27 2017 *)
  • PARI
    { for (n=1, 1000, write("b064661.txt", n, " ", n - prime(n)\log(prime(n))) ) } \\ Harry J. Smith, Sep 21 2009

A204594 Nearest integer to n*log(n) + n*log(log(n)) - n + n/log(n)*(log(log(n))-2) - n*log(log(n))*(log(log(n))-6)/(2 log(n)^2), an asymptotic expression for prime(n).

Original entry on oeis.org

-13, -4, 0, 3, 6, 10, 13, 17, 20, 24, 28, 32, 36, 40, 44, 49, 53, 57, 62, 66, 71, 76, 80, 85, 90, 95, 100, 105, 109, 115, 120, 125, 130, 135, 140, 145, 151, 156, 161, 167, 172, 177, 183, 188, 194, 199, 205, 210, 216, 222, 227, 233, 239, 244, 250, 256, 262
Offset: 2

Views

Author

M. F. Hasler, Feb 07 2012

Keywords

Links

Crossrefs

Cf. A059112, A059111, A064658, A064659.

Programs

  • Mathematica
    Table[Round[n Log[n] + n Log[Log[n]] - n + n/Log[n](Log[Log[n]] - 2) - n Log[Log[n]](Log[Log[n]] - 6)/(2 Log[n]^2)], {n, 2, 58}] (* Alonso del Arte, Feb 07 2012 *)
  • PARI
    A204594(n)=round(n*log(n)+n*log(log(n))-n+n/log(n)*(log(log(n))-2)-n*log(log(n))/2/log(n)^2*(log(log(n))-6))
Showing 1-6 of 6 results.

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

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