A323908 Reversing binary representation of A004718, Per Nørgård's "infinity sequence".

0, 1, 3, 2, 1, 0, 6, 7, 3, 2, 0, 1, 2, 3, 5, 4, 1, 0, 6, 7, 0, 1, 3, 2, 6, 7, 1, 0, 7, 6, 12, 13, 3, 2, 0, 1, 2, 3, 5, 4, 0, 1, 3, 2, 1, 0, 6, 7, 2, 3, 5, 4, 3, 2, 0, 1, 5, 4, 2, 3, 4, 5, 15, 14, 1, 0, 6, 7, 0, 1, 3, 2, 6, 7, 1, 0, 7, 6, 12, 13, 0, 1, 3, 2, 1, 0, 6, 7, 3, 2, 0, 1, 2, 3, 5, 4, 6, 7, 1, 0, 7, 6, 12, 13, 1, 0

Offset

0,3

Comments

The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65536

Index entries for sequences related to binary expansion of n

Formula

If A004718(n) <= 0, a(n) = A048724(-A004718(n)), otherwise a(n) = A065621(A004718(n)).

For all n >= 1, A065620(a(n)) = A004718(n).

Prog

(PARI)
up_to = 65536;
A004718list(up_to) = { my(v=vector(up_to)); v[1]=1; v[2]=-1; for(n=3, up_to, v[n] = if(n%2, 1+v[n>>1], -v[n/2])); (v); }; \\ After code in A004718.
v004718 = A004718list(up_to);
A004718(n) = if(!n, n, v004718[n]);
A048724(n) = bitxor(n, n<<1);
A065621(n) = bitxor(n-1, n+n-1);
A323908(n) = if(A004718(n)<=0, A048724(-A004718(n)), A065621(A004718(n)));
(Python)
from itertools import groupby
def A323908(n):
    c = 0
    for k, g in groupby(bin(n)[2:]):
        c = c+len(list(g)) if k == '1' else (-c if len(list(g))&1 else c)
    return -c^(-c<<1) if c<=0 else c^(c&~-c)<<1 # Chai Wah Wu, Mar 02 2023

Crossrefs

Cf. A004718, A048724, A065620, A065621, A083866 (positions of zeros), A323907 (rgs-transform), A323909.

Sequence in context: A194753 A359400 A373072 * A098825 A111460 A035327

Adjacent sequences: A323905 A323906 A323907 * A323909 A323910 A323911

Keyword

nonn

Author

Antti Karttunen, Feb 09 2019

Status

approved