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 1-3 of 3 results.

A081477 Complement of A086377.

Original entry on oeis.org

2, 3, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 26, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 108, 109, 111, 113, 114, 116, 118
Offset: 1

Views

Author

N. J. A. Sloane, Oct 12 2008

Keywords

Comments

The old entry with this sequence number was a duplicate of A003687.
Is A086377 the sequence of positions of 1 in A189687? - Clark Kimberling, Apr 25 2011
The answer to Kimberling's question is: yes. See the Bosma-Dekking-Steiner paper. - Michel Dekking, Oct 14 2018

Links

Crossrefs

Cf. A086377, A004641, A189687.

Programs

  • Mathematica
    t = Nest[Flatten[# /. {0->{0,1,1}, 1->{0,1}}] &, {0}, 5] (*A189687*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A086377 conjectured *)
Flatten[Position[t, 1]] (* A081477 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189688*)
(* Clark Kimberling, Apr 25 2011 *)

Formula

Conjectures from Clark Kimberling, Aug 03 2022: (Start)
[a(n)*r] = n + [n*r] for n >= 1, where r = sqrt(2) and [ ] = floor.
{a(n)*sqrt(2)} > 1/2 if n is in A120753, where { } = fractional part; otherwise n is in A120752. (End)

Extensions

Name corrected by Michel Dekking, Jan 04 2019

A120753 Numbers k such that {rk} > c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.

Original entry on oeis.org

1, 4, 5, 7, 8, 11, 14, 15, 18, 21, 22, 24, 25, 28, 29, 31, 32, 35, 38, 39, 41, 42, 45, 46, 48, 49, 52, 55, 56, 59, 62, 63, 65, 66, 69, 72, 73, 76, 79, 80, 82, 83, 86, 87, 89, 90, 93, 96, 97, 100, 103, 104, 106, 107, 110, 113, 114, 117, 120, 121, 123, 124, 127, 128, 130, 131
Offset: 1

Views

Author

Clark Kimberling, Jul 01 2006

Keywords

Comments

Positions of 1 in A083035.

Examples

			(See A120243.)

Crossrefs

Cf. A083035, A120752, A190762.

Programs

  • Mathematica
    r = Sqrt[1/2]; b = 2; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A083035 *)
Flatten[Position[t, 0]]      (* A120752 *)
Flatten[Position[t, 1]]      (* A120753 *)

A090892 Solutions x to equation floor(x*r*floor(x/r)) = floor(x/r*floor(x*r)) when r = sqrt(2).

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 10, 12, 13, 16, 17, 19, 20, 23, 26, 27, 30, 33, 34, 36, 37, 40, 43, 44, 47, 50, 51, 53, 54, 57, 58, 60, 61, 64, 67, 68, 70, 71, 74, 75, 77, 78, 81, 84, 85, 88, 91, 92, 94, 95, 98, 99, 101, 102, 105, 108, 109, 111, 112, 115, 116, 118, 119, 122, 125, 126
Offset: 0

Views

Author

Benoit Cloitre, Feb 15 2004

Keywords

Comments

Terms >= 2 give numbers n satisfying: floor(sqrt(2)*n) is even. - Benoit Cloitre, May 27 2004
Essentially equivalent to A120752, see Fried link. - Charles R Greathouse IV, Jan 20 2023

Links

Crossrefs

Cf. A001951, A002193, A120752.

Programs

  • Mathematica
    With[{r = Sqrt[2]}, Select[Range[0, 150], Floor[#*r*Floor[#/r]] == Floor[(#/r)*Floor[#*r]] &]] (* G. C. Greubel, Feb 06 2019 *)
  • PARI
    r=sqrt(2); for(n=0,150, if(floor(n*r*floor(n/r))==floor(n/r*floor(n*r)), print1(n, ", "))) \\ G. C. Greubel, Feb 06 2019

Formula

It seems that a(n) = 2*n + o(n); conjecture : a(n) = 2*n + O(1).
Showing 1-3 of 3 results.

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

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