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A247356 Numbers k such that d(r,k) = 1 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
3, 5, 7, 16, 17, 19, 22, 23, 30, 32, 33, 41, 45, 49, 56, 61, 67, 74, 75, 76, 88, 90, 91, 98, 99, 101, 105, 108, 115, 116, 117, 120, 125, 131, 137, 138, 140, 141, 154, 158, 164, 167, 170, 172, 175, 178, 185, 188, 189, 193, 194, 199, 203, 221, 230, 231, 234 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..1115

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) = 3 and a(2) = 5.

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, A246357, A246358.

Sequence in context: A005540 A155802 A080741 * A073436 A291736 A010070

Adjacent sequences:  A247353 A247354 A247355 * A247357 A247358 A247359

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 17 2014

STATUS

approved

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Last modified February 25 05:15 EST 2020. Contains 332217 sequences. (Running on oeis4.)