A338691 - OEIS

%I #30 Dec 12 2021 02:21:40

%S 2,3,7,8,10,11,12,15,18,19,23,26,27,28,31,32,34,35,39,40,42,43,44,47,

%T 48,50,51,55,58,59,60,63,66,67,71,72,74,75,76,79,82,83,87,90,91,92,95,

%U 98,99,103,104,106,107,108,111,112,114,115,119,122,123,124,127,128

%N Positions of (-1)'s in A209615.

%C Also positions of 2's and 3's in A003324.

%C Also positions of 1's in A292077. - _Jianing Song_, Nov 27 2021

%C Numbers of the form (2*k+1) * 2^e where k+e is odd. In other words, union of {(4*m+1) * 2^(2t+1)} and {(4*m+3) * 2^(2t)}, where m >= 0, t >= 0.

%C Numbers whose quaternary (base-4) expansion ends in 300...00 or 0200..00 or 2200..00. Trailing 0's are not necessary.

%C There are precisely 2^(N-1) terms <= 2^N for every N >= 1.

%C Equals A004767 Union A343500.

%C Complement of A338692. - _Jianing Song_, Apr 26 2021

%H Jianing Song, <a href="/A338691/b338691.txt">Table of n, a(n) for n = 1..8192</a>

%H Kevin Ryde, <a href="http://user42.tuxfamily.org/alternate/index.html">Iterations of the Alternate Paperfolding Curve</a>, see index "TurnRight" with a(n) = TurnRight(n-1).

%F a(n) = A343501(n)/2. - _Jianing Song_, Apr 26 2021

%e 15 is a term since it is in the family {(4*m+3) * 2^(2t)} with m = 3, t = 0.

%e 18 is a term since it is in the family {(4*m+1) * 2^(2t+1)} with m = 2, t = 0.

%o (PARI) isA338691(n) = my(e=valuation(n, 2), k=bittest(n, e+1)); (k+e)%2

%Y Cf. A209615, A338692 (positions of 1's), A004767 (the odd terms), A343500 (the even terms), A003324, A292077, A343501.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Apr 24 2021