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A323908 Reversing binary representation of A004718, Per Nørgård's "infinity sequence". 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.
LINKS
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 09 2019
STATUS
approved

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Last modified July 20 14:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)