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A103391 'Even' fractal sequence for the natural numbers: Deleting every even-index term results in the same sequence. 20
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A003602 is the 'odd' fractal sequence for the natural numbers.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..10000 from Reinhard Zumkeller)

FORMULA

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

MAPLE

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

PROG

(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

CROSSREFS

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

KEYWORD

easy,nonn

AUTHOR

Eric Rowland, Mar 20 2005

EXTENSIONS

Data section extended up to a(105) to better differentiate from several nearby sequences. - Antti Karttunen, Feb 05 2020

STATUS

approved

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Last modified July 3 04:45 EDT 2022. Contains 355030 sequences. (Running on oeis4.)