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.

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

1,2

Comments

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..2000

Example

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.

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 *)

Crossrefs

Cf. A247524, A247519.

Sequence in context: A054353 A284555 A031948 * A169957 A165712 A325390

Adjacent sequences: A247520 A247521 A247522 * A247524 A247525 A247526

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 19 2014

Status

approved