A101267 a(1) = 1; a(n) = a(2^ceiling(log_2(n)) + 1 - n)th smallest positive integer not yet in the sequence.
1, 2, 4, 3, 7, 9, 6, 5, 13, 15, 19, 17, 11, 14, 10, 8, 24, 27, 32, 29, 37, 40, 35, 33, 21, 23, 30, 26, 18, 22, 16, 12, 44, 49, 56, 52, 62, 67, 59, 57, 73, 76, 82, 79, 69, 74, 66, 63, 39, 43, 50, 46, 58, 64, 54, 51, 34, 38, 47, 42, 28, 36, 25, 20, 84, 90, 102, 94, 110, 116, 106
Offset: 1
Examples
Since 2^ceiling(log_2(n)) +1 -n = 3 at n = 6, a(6) = the a(3)th (the 4th) smallest positive integer not among the first 5 terms of the sequence. The positive integers not among the first 5 terms are 5,6,8,9,10,... The 4th of these is 9, which is a(6).
Links
- Ivan Neretin, Table of n, a(n) for n = 1..8192
Programs
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Mathematica
a[1] = 1; a[n_] := a[n] = Complement[ Range[100], Table[ a[i], {i, n - 1}]] [[ a[2^Ceiling[ Log[2, n]] + 1 - n]]]; Table[ a[n], {n, 71}] (* Robert G. Wilson v, Jan 13 2005 *)
Extensions
More terms from Robert G. Wilson v, Jan 13 2005
Comments