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.

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

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 * A291736 A010070 A291107

Adjacent sequences: A247353 A247354 A247355 * A247357 A247358 A247359

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 17 2014

Status

approved