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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A299380 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

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)