login
A338692
Positions of 1's in A209615.
6
1, 4, 5, 6, 9, 13, 14, 16, 17, 20, 21, 22, 24, 25, 29, 30, 33, 36, 37, 38, 41, 45, 46, 49, 52, 53, 54, 56, 57, 61, 62, 64, 65, 68, 69, 70, 73, 77, 78, 80, 81, 84, 85, 86, 88, 89, 93, 94, 96, 97, 100, 101, 102, 105, 109, 110, 113, 116, 117, 118, 120, 121, 125, 126
OFFSET
1,2
COMMENTS
Also positions of 1's and 4's in A003324.
Also positions of 0's in A292077. - Jianing Song, Nov 27 2021
Numbers of the form (2*k+1) * 2^e where k+e is even. In other words, union of {(4*m+1) * 2^(2t)} and {(4*m+3) * 2^(2t+1)}, where m >= 0, t >= 0.
Numbers whose quaternary (base-4) expansion ends in 100...00 or 1200..00 or 3200..00. Trailing 0's are not necessary.
There are precisely 2^(N-1) terms <= 2^N for every N >= 1.
Equals A016813 Union A343501.
Complement of A338691. - Jianing Song, Apr 26 2021
LINKS
Kevin Ryde, Iterations of the Alternate Paperfolding Curve, see index "TurnLeft" with a(n) = TurnLeft(n-1).
FORMULA
a(n) = A343500(n)/2. - Jianing Song, Apr 26 2021
EXAMPLE
14 is a term since it is in the family {(4*m+3) * 2^(2t+1)} with m = 1, t = 0.
16 is a term since it is in the family {(4*m+1) * 2^(2t)} with m = 0, t = 2.
PROG
(PARI) isA338692(n) = my(e=valuation(n, 2), k=bittest(n, e+1)); !((k+e)%2)
CROSSREFS
Cf. A209615, A338691 (positions of (-1)'s), A016813 (the odd terms), A343501 (the even terms), A003324, A292077, A343500.
Sequence in context: A245236 A209122 A073263 * A039013 A241511 A020669
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Apr 24 2021
STATUS
approved