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A243071
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Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A064989(2n+1)).
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52
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0, 1, 3, 2, 7, 6, 15, 4, 5, 14, 31, 12, 63, 30, 13, 8, 127, 10, 255, 28, 29, 62, 511, 24, 11, 126, 9, 60, 1023, 26, 2047, 16, 61, 254, 27, 20, 4095, 510, 125, 56, 8191, 58, 16383, 124, 25, 1022, 32767, 48, 23, 22, 253, 252, 65535, 18, 59, 120, 509, 2046, 131071
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OFFSET
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1,3
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COMMENTS
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Note the indexing: the domain starts from 1, while the range includes also zero.
See also the comments at A163511, which is the inverse permutation to this one.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..1024
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A064989(2n+1)).
For n >= 1, a(A000040(n)) = A000225(n).
For n >= 1, a(2n+1) = 1 + 2*a(A064216(n+1)).
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PROG
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(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)
(definec (A243071 n) (cond ((<= n 2) (- n 1)) ((even? n) (* 2 (A243071 (/ n 2)))) (else (+ 1 (* 2 (A243071 (A064989 n)))))))
(Python)
from functools import reduce
from sympy import factorint, prevprime
from operator import mul
def a064989(n):
f = factorint(n)
return 1 if n==1 else reduce(mul, (1 if i==2 else prevprime(i)**f[i] for i in f))
def a(n): return n - 1 if n<3 else 2*a(n//2) if n%2==0 else 1 + 2*a(a064989(n))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 15 2017
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CROSSREFS
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Inverse: A163511.
Cf. A000040, A000225, A064989, A064216.
Sequence in context: A056481 A269386 A252756 * A332811 A286556 A243354
Adjacent sequences: A243068 A243069 A243070 * A243072 A243073 A243074
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jun 20 2014
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STATUS
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approved
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