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A052330
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Let S_k denote the first 2^k terms of this sequence and let b_k be the smallest positive integer that is not in S_k; then the numbers b_k*S_k are the next 2^k terms.
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19
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1, 2, 3, 6, 4, 8, 12, 24, 5, 10, 15, 30, 20, 40, 60, 120, 7, 14, 21, 42, 28, 56, 84, 168, 35, 70, 105, 210, 140, 280, 420, 840, 9, 18, 27, 54, 36, 72, 108, 216, 45, 90, 135, 270, 180, 360, 540, 1080, 63, 126, 189, 378, 252, 504, 756, 1512, 315, 630, 945, 1890
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Inverse of sequence A064358 considered as a permutation of the positive integers. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
This sequence is not exactly a permutation because it has offset 0 but doesn't contain 0. A052331 is its exact inverse, which has offset 1 and contains 0. See also A064358.
Are there any other values of n besides 4 and 36 with a(n) = n? - Tomasz Ordowski (ordot(AT)poczta.onet.pl), Apr 01 2005
4=100=4^1*3^0*2^0, 36=100100=9^1*7^0*5^0*4^1*3^0*2^0. - Tomasz Ordowski (ordot(AT)poczta.onet.pl), May 26 2005
[Daniel Forgues, Feb 11 2011]: (Start)
Ordering of positive integers by increasing "Fermi-Dirac representation", which is a representation of the "Fermi-Dirac factorization", term implying that each prime power with a power of two as exponent may appear at most once in the "Fermi-Dirac factorization" of n. (Cf. comment in A050376)(see also the OEIS Wiki page) (End)
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1023
Index entries for sequences that are permutations of the natural numbers
OEIS Wiki, Ordering of positive integers by increasing "Fermi-Dirac representation"
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FORMULA
| a(0)=1; a(n+2^k)=a(n)*b(k) for n<2^k, k=0, 1, ... where b is A050376. - Tomasz Ordowski (ordot(AT)poczta.onet.pl), Mar 04 2005
[Daniel Forgues, Feb 12 2011]: (Start) The binary representation of n,
n = Sum(i=0..1+floor(log_2(n)) n_i * 2^i, n_i in {0,1}, is taken as the "Fermi-Dirac representation" (A182979) of a(n),
a(n) = Prod(i=0..1+floor(log_2(n)) (b_i)^(n_i) where b_i is A050376(i), i.e. the i_th "Fermi-Dirac prime" (prime power with exponent being a power of 2). (End)
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EXAMPLE
| Terms following 5 are 10,15,30,20,40,60,120; this is followed by 7 as 6 has already occurred.
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CROSSREFS
| Cf. A050376, A182979, A052331, A096111, A096113, A096114, A096115, A096116, A096118, A096119, A050030.
Sequence in context: A083872 A121663 A096112 * A059900 A123664 A084980
Adjacent sequences: A052327 A052328 A052329 * A052331 A052332 A052333
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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EXTENSIONS
| Entry revised Mar 17 2005 by N. J. A. Sloane (njas(AT)research.att.com), based on comments from several people, especially David Wasserman (wasserma(AT)spawar.navy.mil) and Tom Ordowski (ordot(AT)poczta.onet.pl)
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