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A254118
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Permutation of natural numbers: a(n) = A249745(1+A254103(n)) - 1.
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4
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1, 2, 3, 6, 5, 4, 8, 20, 11, 7, 9, 33, 18, 23, 14, 13, 30, 36, 21, 44, 10, 29, 15, 55, 53, 28, 16, 74, 39, 41, 12, 179, 90, 96, 50, 114, 24, 42, 35, 92, 69, 47, 19, 86, 25, 51, 26, 236, 153, 110, 81, 101, 22, 45, 48, 221, 113, 119, 56, 77, 65, 38, 17, 546, 182
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (A254116((2*n)+1)-1) / 2. [Obtained also from the odd bisection of A254116.]
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PROG
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(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)};
for(n=1, 8191, write("b254118.txt", n, " ", A254118(n)));
(Scheme, two versions)
(Python)
from sympy import factorint, prevprime, floor
from operator import mul
from functools import reduce
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 a254116(n): return a064216(a254103(n))
def a(n): return (a254116(2*n + 1) - 1)//2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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