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 1-5 of 5 results.

A293328 Least integer k such that k/2^n > sqrt(1/3).

Original entry on oeis.org

1, 2, 3, 5, 10, 19, 37, 74, 148, 296, 592, 1183, 2365, 4730, 9460, 18919, 37838, 75675, 151349, 302698, 605396, 1210792, 2421583, 4843166, 9686331, 19372661, 38745321, 77490642, 154981283, 309962566, 619925132, 1239850263, 2479700525, 4959401050, 9918802099
Offset: 0

Views

Author

Clark Kimberling, Oct 10 2017

Keywords

Links

Crossrefs

Cf. A002194, A094386, A293327, A293329.

Programs

  • Mathematica
    z = 120; r = Sqrt[1/3];
Table[Floor[r*2^n], {n, 0, z}];   (* A293327 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293328 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293329 *)

Formula

a(n) = ceiling(r*2^n), where r = sqrt(1/3).
a(n) = A293327(n) + 1.

A293327 Greatest integer k such that k/2^n < sqrt(1/3).

Original entry on oeis.org

0, 1, 2, 4, 9, 18, 36, 73, 147, 295, 591, 1182, 2364, 4729, 9459, 18918, 37837, 75674, 151348, 302697, 605395, 1210791, 2421582, 4843165, 9686330, 19372660, 38745320, 77490641, 154981282, 309962565, 619925131, 1239850262, 2479700524, 4959401049, 9918802098
Offset: 0

Views

Author

Clark Kimberling, Oct 09 2017

Keywords

Links

Crossrefs

Cf. A002194, A094386, A293328, A293329.

Programs

  • Mathematica
    z = 120; r = Sqrt[1/3];
Table[Floor[r*2^n], {n, 0, z}];   (* A293327 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293328 *)
Table[Round[r*2^n], {n, 0, z}];   (* A293329 *)

Formula

a(n) = floor(r*2^n), where r = sqrt(1/3).
a(n) = A293328(n) - 1.

Extensions

Definition and formula corrected by Clark Kimberling, Dec 26 2022

A293329 The integer k that minimizes |k/2^n - sqrt(1/3)|.

Original entry on oeis.org

1, 1, 2, 5, 9, 18, 37, 74, 148, 296, 591, 1182, 2365, 4730, 9459, 18919, 37837, 75674, 151349, 302698, 605396, 1210791, 2421583, 4843165, 9686330, 19372660, 38745321, 77490641, 154981283, 309962566, 619925131, 1239850262, 2479700525, 4959401049, 9918802098
Offset: 0

Views

Author

Clark Kimberling, Oct 10 2017

Keywords

Links

Crossrefs

Cf. A002194, A094386, A293327, A293328.

Programs

  • Mathematica
    z = 120; r = Sqrt[1/3];
Table[Floor[r*2^n], {n, 0, z}];   (* A293327 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293328 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293329 *)

Formula

a(n) = floor(1/2 + r*2^n), where r = sqrt(1/3).
a(n) = A293327(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293328(n).

A293325 Least integer k such that k/2^n > sqrt(3).

Original entry on oeis.org

2, 4, 7, 14, 28, 56, 111, 222, 444, 887, 1774, 3548, 7095, 14189, 28378, 56756, 113512, 227024, 454047, 908094, 1816187, 3632374, 7264748, 14529496, 29058991, 58117982, 116235963, 232471925, 464943849, 929887697, 1859775394, 3719550787, 7439101574
Offset: 0

Views

Author

Clark Kimberling, Oct 09 2017

Keywords

Links

Crossrefs

Cf. A002194, A094386, A293326.

Programs

  • Mathematica
    z = 120; r = Sqrt[3];
Table[Floor[r*2^n], {n, 0, z}];   (* A094386 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293325 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293326 *)
  • Python
    from math import isqrt
def A293325(n): return 1+isqrt(3*(1<<(n<<1))) # Chai Wah Wu, Jul 28 2022

Formula

a(n) = ceiling(r*2^n), where r = sqrt(3).
a(n) = A094386(n) + 1.

A293326 The integer k that minimizes |k/2^n - sqrt(3)|.

Original entry on oeis.org

2, 3, 7, 14, 28, 55, 111, 222, 443, 887, 1774, 3547, 7094, 14189, 28378, 56756, 113512, 227023, 454047, 908093, 1816187, 3632374, 7264748, 14529495, 29058991, 58117981, 116235962, 232471924, 464943848, 929887697, 1859775393, 3719550787, 7439101574
Offset: 0

Views

Author

Clark Kimberling, Oct 09 2017

Keywords

Links

Crossrefs

Cf. A002194, A094386, A293325.

Programs

  • Mathematica
    z = 120; r = Sqrt[3];
Table[Floor[r*2^n], {n, 0, z}];   (* A094386 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293325 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293326 *)
  • Python
    from math import isqrt
def A293326(n): return (k:=isqrt(m:=3*(1<<(n<<1))))+int((m-k*(k+1)<<2)-1>=0) # Chai Wah Wu, Jul 28 2022

Formula

a(n) = floor(1/2 + r*2^n), where r = sqrt(3).
a(n) = A094386(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293325(n).
Showing 1-5 of 5 results.

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

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