cp's OEIS Frontend

A247522 Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.

%I A247522 #9 Sep 26 2014 21:12:16
%S A247522 1,5,6,7,12,15,16,19,20,21,25,28,29,35,36,37,38,39,40,51,52,53,54,65,
%T A247522 66,67,68,72,73,77,78,82,91,101,102,106,107,110,113,114,124,151,152,
%U A247522 155,160,161,162,163,164,168,169,179,180,193,194,195,196,197,203
%N A247522 Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
%C A247522 Every positive integer lies in exactly one of these: A247519, A247520, A247521.
%H A247522 Clark Kimberling, <a href="/A247522/b247522.txt">Table of n, a(n) for n = 1..1000</a>
%e A247522 r has binary digits 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, ...
%e A247522 s has binary digits 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, ...
%e A247522 so that a(1) = 1 and a(2) = 5.
%t A247522 z = 400; r1 = GoldenRatio; r = FractionalPart[r1]; s = FractionalPart[r1/2];
%t A247522 u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
%t A247522 v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
%t A247522 t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247522 t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247522 t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t A247522 t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t A247522 Flatten[Position[t1, 1]] (* A247519 *)
%t A247522 Flatten[Position[t2, 1]] (* A247520 *)
%t A247522 Flatten[Position[t3, 1]] (* A247521 *)
%t A247522 Flatten[Position[t4, 1]] (* A247522 *)
%Y A247522 Cf. A247519, A247520, A247521.
%K A247522 nonn,easy,base
%O A247522 1,2
%A A247522 _Clark Kimberling_, Sep 19 2014