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A247632 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(8)}, and { } = fractional part. 5
1, 4, 6, 12, 15, 21, 25, 29, 38, 42, 48, 52, 55, 60, 64, 66, 70, 72, 78, 83, 86, 89, 93, 96, 100, 102, 104, 107, 109, 111, 113, 119, 122, 130, 134, 136, 139, 144, 151, 153, 157, 159, 163, 166, 169, 173, 177, 179, 184, 187, 191, 195, 198, 202, 204, 209, 211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..1097

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, A247633, A247634.

Sequence in context: A074870 A251630 A256241 * A104236 A265225 A122781

Adjacent sequences:  A247629 A247630 A247631 * A247633 A247634 A247635

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Sep 23 2014

STATUS

approved

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Last modified January 19 04:17 EST 2020. Contains 331031 sequences. (Running on oeis4.)