A264974 Self-inverse permutation of natural numbers: a(n) = A263273(4*n) / 4.

0, 1, 2, 3, 4, 5, 6, 7, 16, 9, 10, 19, 12, 13, 14, 15, 8, 17, 18, 11, 20, 21, 34, 43, 48, 25, 52, 27, 28, 55, 30, 37, 46, 57, 22, 49, 36, 31, 58, 39, 40, 41, 42, 23, 50, 45, 32, 59, 24, 35, 44, 51, 26, 53, 54, 29, 56, 33, 38, 47, 60, 61, 142, 63, 88, 169, 102, 115, 124, 129, 70, 151, 144, 97, 178, 75, 106, 133, 156, 79, 160, 81

Offset: 0

Author

Antti Karttunen, Dec 05 2015

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..4921
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Terms of A264986 halved.

Cf. A263272, A263273, A264978.

Cf. also A264975, A264976.

Programs

Python

from sympy import factorint
from sympy.ntheory.factor_ import digits
from operator import mul
def a030102(n): return 0 if n==0 else int(''.join(map(str, digits(n, 3)[1:][::-1])), 3)
def a038502(n):
    f=factorint(n)
    return 1 if n==1 else reduce(mul, [1 if i==3 else i**f[i] for i in f])
def a038500(n): return n/a038502(n)
def a263273(n): return 0 if n==0 else a030102(a038502(n))*a038500(n)
def a(n): return a263273(4*n)/4 # Indranil Ghosh, May 25 2017

Formula

a(n) = A263273(4*n) / 4.

a(n) = A264986(n) / 2 = A263272(2*n) / 2.

As a composition of related permutations:

a(n) = A264975(A263272(n)) = A263272(A264976(n)).

Other identities. For all n >= 0:

a(3*n) = 3*a(n).

A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

A264978(n) = a(2n)/2. [Thus the restriction onto even numbers induces yet another permutation.]