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A247520 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part. 4
2, 8, 13, 17, 22, 26, 30, 33, 41, 43, 46, 48, 55, 61, 63, 69, 74, 79, 83, 92, 99, 103, 108, 111, 115, 118, 125, 127, 133, 138, 144, 148, 153, 156, 158, 165, 170, 172, 176, 181, 184, 187, 189, 198, 204, 207, 212, 214, 216, 221, 227, 229, 235, 242, 248, 250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every positive integer lies in exactly one of these: A247519, A247520, A247521, A247522.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

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) = 2.

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]]

t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];

t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];

t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];

t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];

Flatten[Position[t1, 1]] (* A247519 *)

Flatten[Position[t2, 1]] (* A247520 *)

Flatten[Position[t3, 1]] (* A247521 *)

Flatten[Position[t4, 1]] (* A247522 *)

CROSSREFS

Cf. A247519, A247521, A247522.

Sequence in context: A030389 A136738 A288227 * A304801 A184519 A156245

Adjacent sequences:  A247517 A247518 A247519 * A247521 A247522 A247523

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 19 2014

STATUS

approved

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)