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 1-2 of 2 results.

A247523 Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.

Original entry on oeis.org

1, 3, 5, 6, 7, 9, 10, 12, 15, 16, 19, 20, 21, 23, 25, 28, 29, 31, 35, 36, 37, 38, 39, 40, 44, 49, 51, 52, 53, 54, 56, 57, 58, 59, 65, 66, 67, 68, 70, 72, 73, 75, 77, 78, 80, 82, 84, 85, 86, 87, 88, 89, 91, 93, 94, 95, 96, 97, 101, 102, 104, 106, 107, 110
Offset: 1

Views

Author

Clark Kimberling, Sep 19 2014

Keywords

Comments

Every positive integer lies in exactly one of the sequences A247423 and A247524.

Examples

			r has binary digits 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, ...
so that a(1) = 1 and a(2) = 3.
		

Crossrefs

Programs

  • Mathematica
    z = 400; r1 = GoldenRatio; r = FractionalPart[r1]; s = FractionalPart[r1/2];
    u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
    v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
    t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
    Flatten[Position[t, 1]]  (* A247523 *)
    Flatten[Position[t, 0]]  (* A247524 *)

A247636 Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 12, 13, 15, 19, 21, 23, 25, 27, 29, 36, 38, 41, 42, 46, 48, 50, 52, 53, 55, 56, 60, 61, 64, 65, 66, 68, 70, 71, 72, 77, 78, 80, 83, 84, 86, 88, 89, 91, 93, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 118
Offset: 1

Views

Author

Clark Kimberling, Sep 23 2014

Keywords

Comments

Every positive integer lies in exactly one of the sequences A247635 and A247636.

Examples

			r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 1 and a(2) = 3.
		

Crossrefs

Programs

  • Mathematica
    z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
    u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
    v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
    t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
    Flatten[Position[t, 1]]  (* A247635 *)
    Flatten[Position[t, 0]]  (* A247636 *)
Showing 1-2 of 2 results.