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
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.
Links
- Clark Kimberling, Table of n, a(n) for n = 1..2000
Programs
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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 *)
Comments