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 1-9 of 9 results.

A140138 Numbers n such that A140080(n) = 2.

Original entry on oeis.org

5, 10, 17, 20, 34, 40, 65, 68, 80, 130, 136, 160, 257, 260, 272, 320, 341, 514, 520, 544, 640, 682, 1025, 1028, 1040, 1088, 1109, 1280, 1301, 1349, 1361, 1364, 2050, 2056, 2080, 2176, 2218, 2560, 2602, 2698, 2722, 2728, 4097, 4100, 4112, 4160
Offset: 1

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 08 2008

Keywords

Crossrefs

Cf. A140080, A140137.

A140086 Same as A140080, except now e=9.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 2, 3, 1, 0, 2, 1, 2, 1, 3, 2, 1, 2, 0, 1, 2, 3, 1, 2, 2, 1, 1, 0, 3, 2, 2, 1, 1, 2, 2, 3, 0, 1, 1, 2, 2, 1, 3, 2, 1, 0, 2, 1, 2, 3, 1, 2, 1, 2, 0, 1, 3, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 3, 2, 3, 3, 4, 0, 1, 1, 2, 1, 2, 2, 3, 2, 0, 1, 1, 3, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 2, 2, 3, 3
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

Links

A140082 Same as A140080, except now e=5.

Original entry on oeis.org

0, 1, 1, 2, 1, 0, 2, 1, 1, 2, 0, 1, 2, 1, 1, 0, 1, 2, 2, 3, 0, 1, 1, 2, 2, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 2, 1, 3, 1, 0, 1, 1, 1, 1, 0, 2, 1, 2, 3, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 0, 1, 2, 1, 1, 0, 3, 2, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 2, 1, 3
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

Links

Programs

  • Fortran
    ! See link in A140080 for Fortran program.

A140083 Same as A140080, except now e=6.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 0, 1, 2, 3, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 2, 3, 0, 1, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 3, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 3, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

Links

A140084 Same as A140080, except now e=7.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 3, 2, 3, 0, 1, 1, 2, 2, 3, 2, 0, 3, 1, 2, 3, 3, 4, 0, 1, 1, 2, 1, 2, 2, 0, 2, 3, 3, 1, 2, 3, 0, 1, 3, 4, 1, 2, 2, 0, 3, 1, 3, 1, 4, 2, 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 3, 2, 3, 0, 1, 2, 3, 3, 4, 3, 0, 1, 1, 2, 3, 3, 4, 0, 1, 1, 2, 3, 4, 4, 0, 1, 1, 2, 1, 2, 3, 0
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

Links

A140137 Numbers n such that A140080(n) = 1.

Original entry on oeis.org

1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 22, 23, 25, 26, 28, 29, 31, 32, 35, 37, 38, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 67, 70, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104, 106, 107, 109, 110
Offset: 1

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 08 2008

Keywords

Comments

This and A140138 together give all numbers not divisible by 3.

Crossrefs

Cf. A140080, A140138.

A140200 Partial sums of A140080.

Original entry on oeis.org

0, 1, 2, 2, 3, 5, 5, 6, 7, 7, 9, 10, 10, 11, 12, 12, 13, 15, 15, 16, 18, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 28, 29, 29, 30, 31, 31, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 46, 47, 48, 48, 49, 51, 51, 52, 54, 54, 55, 56, 56, 57, 58
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 09 2008

Keywords

A140081 Period 4: repeat [0, 1, 1, 2].

Original entry on oeis.org

0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

Comments

Also fix e = 4; then a(n) = minimal Hamming distance between the binary representation of n and the binary representation of any multiple k*e (0 <= k <= n/e) which is a child of n.
A number m is a child of n if the binary representation of n has a 1 in every position where the binary representation of m has a 1.

Links

Crossrefs

Cf. A140201. - Reinhard Zumkeller, Feb 21 2010

Programs

Formula

a(n) = 1 + a(n - 1 - a(n-1)) + 2*a(a(n-1)) - 2*a(n-1), a(0)=0. - Ramasamy Chandramouli, Jan 31 2010
a(n) = A047624(n+2) - A047624(n+1) - 1. - Reinhard Zumkeller, Feb 21 2010
a(n) = 1 - cos(Pi*n/2)/2 - sin(Pi*n/2)/2 - (-1)^n/2. - R. J. Mathar, Oct 08 2011
a(n) = ((n mod 4) + (n mod 2))/2. - Gary Detlefs, Apr 21 2012
From Colin Barker, Jan 13 2013: (Start)
a(n) = a(n-4).
G.f.: -x*(2*x^2+x+1) / ((x-1)*(x+1)*(x^2+1)). (End)
a(n) = floor((3*(n mod 4) + 1)/4). - Wesley Ivan Hurt, Mar 27 2014
From Wesley Ivan Hurt, Apr 22 2015: (Start)
a(n) = floor(1/2 + (n mod 4)/2).
a(n) = 1 - (-1)^n/2 - (-1)^(n/2 - 1/4 + (-1)^n/4)/2. (End)
a(n) = n - floor(n/2) - 2*floor(n/4). - Ridouane Oudra, Oct 30 2019

A140085 Period 8: repeat [0,1,1,2,1,2,2,3].

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1
Offset: 0

Views

Author

Nadia Heninger and N. J. A. Sloane, Jun 03 2008

Keywords

Comments

Also fix e = 8; then a(n) = minimal Hamming distance between the binary representation of n and the binary representation of any multiple ke (0 <= k <= n/e) which is a child of n.
A number m is a child of n if the binary representation of n has a 1 in every position where the binary representation of m has a 1.

Links

Programs

  • Fortran
    ! See link in A140080 for Fortran program.
  • Mathematica
    PadRight[{},100,{0,1,1,2,1,2,2,3}] (* Harvey P. Dale, Jun 16 2025 *)

Formula

a(n) = 3/2 -cos(Pi*n/4)/4 -(1+sqrt(2))*sin(Pi*n/4)/4 -cos(Pi*n/2)/2 -sin(Pi*n/2)/2 -cos(3*Pi*n/4)/4 +(1-sqrt(2))*sin(3*Pi*n/4)/4 -(-1)^n/2. - R. J. Mathar, Oct 08 2011
a(n) = a(n-8). G.f.: -x*(3*x^6+2*x^5+2*x^4+x^3+2*x^2+x+1) / ((x-1)*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Jul 26 2013
Showing 1-9 of 9 results.

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

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