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A246357 Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part. 4
1, 4, 8, 10, 11, 14, 15, 21, 25, 38, 42, 47, 51, 54, 55, 59, 60, 63, 64, 70, 72, 78, 83, 85, 86, 92, 100, 107, 109, 119, 121, 128, 134, 136, 147, 148, 150, 153, 157, 162, 168, 169, 173, 182, 183, 184, 198, 200, 209, 211, 214, 215, 218, 226, 227, 229, 241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every positive integer lies in exactly one of these: A246356, A246357, A246358, A247356.

LINKS

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

EXAMPLE

{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...

{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..

so that a(1) = 1 and a(2) = 4.

MATHEMATICA

z = 500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];

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]]  (* A246356 *)

Flatten[Position[t2, 1]]  (* A246357 *)

Flatten[Position[t3, 1]]  (* A246358 *)

Flatten[Position[t4, 1]]  (* A247356 *)

CROSSREFS

Cf. A247454, A246356, A246358, A247356.

Sequence in context: A288246 A310971 A310972 * A265378 A319606 A235382

Adjacent sequences:  A246354 A246355 A246356 * A246358 A246359 A246360

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 17 2014

STATUS

approved

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Last modified March 29 03:09 EDT 2020. Contains 333104 sequences. (Running on oeis4.)