A247634 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(8)}, and { } = fractional part.

2, 16, 17, 18, 22, 26, 30, 31, 32, 33, 34, 35, 39, 40, 43, 44, 45, 49, 67, 73, 74, 75, 76, 79, 87, 90, 94, 97, 98, 114, 115, 116, 117, 123, 124, 125, 126, 131, 132, 137, 140, 141, 142, 145, 154, 155, 170, 171, 174, 175, 188, 192, 193, 196, 205, 206, 207, 212

Offset

1,1

Comments

Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1122

Example

r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 1 and a(2) = 4.

Mathematica

z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
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]]  (* A247631 *)
Flatten[Position[t2, 1]]  (* A247632 *)
Flatten[Position[t3, 1]]  (* A247633 *)
Flatten[Position[t4, 1]]  (* A247634 *)

Crossrefs

Cf. A247631, A247632, A247633.

Sequence in context: A263355 A066773 A138761 * A261617 A075376 A032935

Adjacent sequences: A247631 A247632 A247633 * A247635 A247636 A247637

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 23 2014

Status

approved