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A103391
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'Even' fractal sequence for the natural numbers: Deleting every even-index term results in the same sequence.
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20
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1, 2, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 14, 8, 15, 5, 16, 9, 17, 2, 18, 10, 19, 6, 20, 11, 21, 4, 22, 12, 23, 7, 24, 13, 25, 3, 26, 14, 27, 8, 28, 15, 29, 5, 30, 16, 31, 9, 32, 17, 33, 2, 34, 18, 35, 10, 36, 19, 37, 6, 38, 20, 39, 11, 40, 21, 41, 4, 42, 22, 43, 12, 44, 23, 45, 7, 46, 24, 47, 13, 48, 25, 49, 3, 50, 26, 51, 14, 52, 27, 53, 8
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OFFSET
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1,2
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COMMENTS
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A003602 is the 'odd' fractal sequence for the natural numbers.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..10000 from Reinhard Zumkeller)
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FORMULA
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For n>1, a(n) = A003602(n-1)+1. - Benoit Cloitre, May 26 2007, indexing corrected by Antti Karttunen, Feb 05 2020
a((2*n-3)*2^p+1) = n, p >= 0 and n >= 2, with a(1) = 1. - Johannes W. Meijer, Jan 28 2013
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MAPLE
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nmax := 82: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 2 to ceil(nmax/(p+2))+1 do a((2*n-3)*2^p+1) := n od: od: a(1) := 1: seq(a(n), n=1..nmax); # Johannes W. Meijer, Jan 28 2013
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PROG
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(Haskell)
-- import Data.List (transpose)
a103391 n = a103391_list !! (n-1)
a103391_list = 1 : ks where
ks = concat $ transpose [[2..], ks]
-- Reinhard Zumkeller, May 23 2013
(PARI)
A003602(n) = (n/2^valuation(n, 2)+1)/2; \\ From A003602
A103391(n) = if(1==n, 1, (1+A003602(n-1))); \\ Antti Karttunen, Feb 05 2020
(Python)
def v(n): b = bin(n); return len(b) - len(b.rstrip("0"))
def b(n): return (n//2**v(n)+1)//2
def a(n): return 1 if n == 1 else 1 + b(n-1)
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, May 29 2022
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CROSSREFS
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Cf. A003602, A220466.
Differs from A331743(n-1) for the first time at n=192, where a(192) = 97, while A331743(191) = 23.
Sequence in context: A323889 A286378 A331745 * A331743 A178804 A322355
Adjacent sequences: A103388 A103389 A103390 * A103392 A103393 A103394
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KEYWORD
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easy,nonn
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AUTHOR
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Eric Rowland, Mar 20 2005
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EXTENSIONS
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Data section extended up to a(105) to better differentiate from several nearby sequences. - Antti Karttunen, Feb 05 2020
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STATUS
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approved
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