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A118315
a(1) = 1. a(2n) = smallest positive integer not occurring among the earlier terms of the sequence. a(2n+1) = the a(n)th positive integer among those positive integers not occurring earlier in the sequence.
4
1, 2, 3, 4, 6, 5, 9, 7, 12, 8, 16, 10, 17, 11, 23, 13, 22, 14, 30, 15, 27, 18, 38, 19, 33, 20, 43, 21, 37, 24, 53, 25, 44, 26, 56, 28, 48, 29, 68, 31, 52, 32, 69, 34, 60, 35, 84, 36, 64, 39, 82, 40, 70, 41, 97, 42, 74, 45, 94, 46, 80, 47, 115, 49, 86, 50, 109, 51
OFFSET
1,2
COMMENTS
Sequence is a permutation of the positive integers.
LINKS
EXAMPLE
For a(9) we want the a(4)th = 4th positive integer among those not equal to any of the first 8 terms of the sequence (those positive integers not equal to 1,2,3,4,6,5,9, or 7). Among those positive integers not equal to any the first 8 terms (which is the sequence 8,10,11,12,13...), 12 is the 4th. So a(9) = 12.
Now for a(10) we want the smallest positive integer that does not occur among the first 9 terms of the sequence. So a(10) = 8.
MATHEMATICA
s={1}; a=Range[1000]; b=Rest[a]; Do[ c=If[OddQ[n], b[[s[[(n-1)/2]]]], b[[1]]]; b=Complement[b, {c}]; AppendTo[s, c], {n, 2, 200}]; s (Seidov)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Apr 23 2006
EXTENSIONS
More terms from Zak Seidov and Joshua Zucker, Apr 23 2006
STATUS
approved