A247457 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.

2, 18, 22, 26, 35, 41, 45, 49, 65, 67, 71, 77, 79, 88, 90, 95, 98, 108, 110, 112, 117, 126, 133, 135, 138, 143, 145, 152, 155, 172, 175, 188, 194, 196, 203, 208, 210, 212, 221, 223, 230, 234, 239, 243, 260, 262, 268, 278, 292, 294, 296, 299, 310, 312, 319

Offset

1,1

Comments

Every positive integer lies in exactly one of these: A247455, A247456, A247457, A247458.

Links

Clark Kimberling, Table of n, a(n) for n = 1..500

Example

{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
so that a(1) = 2.

Mathematica

z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[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]]  (* A247455 *)
Flatten[Position[t2, 1]]  (* A247456 *)
Flatten[Position[t3, 1]]  (* A247457 *)
Flatten[Position[t4, 1]]  (* A247458 *)

Crossrefs

Cf. A247455, A247456, A247458.

Sequence in context: A352159 A266956 A092587 * A015787 A322489 A063430

Adjacent sequences: A247454 A247455 A247456 * A247458 A247459 A247460

Keyword

nonn,easy,base

Author

Clark Kimberling, Sep 18 2014

Status

approved