A140263 Permutation of nonnegative integers obtained by interleaving A117967 and A117968.

0, 1, 2, 5, 7, 3, 6, 4, 8, 17, 22, 15, 21, 16, 23, 11, 19, 9, 18, 10, 20, 14, 25, 12, 24, 13, 26, 53, 67, 51, 66, 52, 68, 47, 64, 45, 63, 46, 65, 50, 70, 48, 69, 49, 71, 35, 58, 33, 57, 34, 59, 29, 55, 27, 54, 28, 56, 32, 61, 30, 60, 31, 62, 44, 76, 42, 75, 43, 77, 38, 73, 36

Offset: 0

Author

Antti Karttunen, May 19 2008, originally described in a posting at the SeqFan mailing list on Sep 15 2005

Keywords

• nonn
• look
• hear

Links

• A. Karttunen, Table of n, a(n) for n = 0..2186
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A140264. Bisections: A117967 & A117968. a(n) = A140265(n+1)-1.

Cf. A004488, A117966.

Programs

Python

from sympy import ceiling
from sympy.ntheory.factor_ import digits
def a004488(n): return int("".join([str((3 - i)%3) for i in digits(n, 3)[1:]]), 3)
def a117968(n):
    if n==1: return 2
    if n%3==0: return 3*a117968(n/3)
    elif n%3==1: return 3*a117968((n - 1)/3) + 2
    else: return 3*a117968((n + 1)/3) + 1
def a117967(n): return 0 if n==0 else a117968(-n) if n<0 else a004488(a117968(n))
def a001057(n): return -(-1)**n*ceiling(n/2)
def a(n): return a117967(a001057(n)) # Indranil Ghosh, Jun 07 2017

Formula

a(n) = A117967(A001057(n)). (Assuming that the domain of A117967 is the whole Z line.)