A254116 Permutation of natural numbers: a(n) = A064216(A254103(n)).

1, 2, 3, 4, 5, 6, 7, 8, 13, 10, 11, 12, 9, 14, 17, 16, 41, 26, 23, 20, 15, 22, 19, 24, 67, 18, 37, 28, 47, 34, 29, 32, 27, 82, 61, 52, 73, 46, 43, 40, 89, 30, 21, 44, 59, 38, 31, 48, 111, 134, 107, 36, 57, 74, 33, 56, 149, 94, 79, 68, 83, 58, 25, 64, 359, 54, 181, 164, 193, 122, 101, 104, 229, 146, 49, 92, 85, 86, 71, 80, 185, 178, 139, 60, 95, 42, 39

Offset: 1

Author

Antti Karttunen, Feb 04 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A254115.

Fixed points: A254099.

Related permutations: A064216, A254103, A254118.

Programs

PARI

default(primelimit, 2^30);
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A064216(n) = A064989((2*n)-1);
A254103(n) = { if(0==n,0,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2)); };
A254116(n) = A064216(A254103(n));
for(n=1, 8192, write("b254116.txt", n, " ", A254116(n)));

Python

from sympy import factorint, prevprime, floor
from operator import mul
def a064216(n):
    f=factorint(2*n - 1)
    return 1 if n==1 else reduce(mul, [prevprime(i)**f[i] for i in f])
def a254103(n):
    if n==0: return 0
    if n%2==0: return 3*a254103(n/2) - 1
    else: return floor((3*(1 + a254103((n - 1)/2)))/2)
def a(n): return a064216(a254103(n)) # Indranil Ghosh, Jun 06 2017

Scheme

(define (A254116 n) (A064216 (A254103 n)))

Formula

a(n) = A064216(A254103(n)).

Other identities. For all n >= 1:

a(n) = a(2n)/2. [Even bisection halved gives back the sequence itself.]

A254118(n) = (a((2*n)+1) - 1)/2. [Likewise, the odd bisection induces A254118.]