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A247522 Numbers k such that d(r,k) = 1 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
1, 5, 6, 7, 12, 15, 16, 19, 20, 21, 25, 28, 29, 35, 36, 37, 38, 39, 40, 51, 52, 53, 54, 65, 66, 67, 68, 72, 73, 77, 78, 82, 91, 101, 102, 106, 107, 110, 113, 114, 124, 151, 152, 155, 160, 161, 162, 163, 164, 168, 169, 179, 180, 193, 194, 195, 196, 197, 203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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) = 1 and a(2) = 5.

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, A247520, A247521.

Sequence in context: A022566 A047320 A327301 * A011761 A106745 A165776

Adjacent sequences:  A247519 A247520 A247521 * A247523 A247524 A247525

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 19 2014

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)