A101319 -id:A101319 - cp's OEIS frontend

A100805 Inverse permutation to sequence A101319 (assuming A101319 is a permutation).

1, 2, 3, 8, 9, 4, 5, 7, 29, 67, 69, 6, 41, 10, 18, 28, 11, 13, 65, 27, 14, 562, 23, 64, 595, 45, 30, 12, 203, 19, 20, 68, 57, 211, 15, 56, 42, 35, 890, 17, 46, 52, 24, 55, 36, 60, 2363, 202, 216, 16, 21, 51, 8159, 31, 32, 26, 2029, 70, 53, 193, 301, 182, 12720, 66, 1004, 25

Offset: 1

Leroy Quet, Jan 04 2005

nonn

a(53), if it exists, is greater than 5000. - Franklin T. Adams-Watters, May 12 2006

David Wasserman, Mar 04 2008, Table of n, a(n) for n = 1..100

Cf. A101319.

More terms from Franklin T. Adams-Watters, May 12 2006

a(53) onwards from David Wasserman, Mar 04 2008

A318578 Let k be the greatest odd divisor of n and let S be the sequence of positive integers not in the sequence so far in increasing order. Then a(n) = S(k).

Original entry on oeis.org

1, 2, 5, 3, 9, 7, 13, 4, 17, 12, 21, 10, 25, 18, 29, 6, 33, 23, 37, 16, 41, 28, 45, 14, 49, 34, 53, 24, 57, 39, 61, 8, 65, 44, 69, 31, 73, 50, 77, 22, 81, 55, 85, 38, 89, 60, 93, 19, 97, 66, 101, 46, 105, 71, 109, 32, 113, 76, 117, 52, 121, 82, 125, 11, 129, 87, 133

Offset: 1

Ivan Neretin, Aug 29 2018

nonn

In other words, a(n) = A000265(n)-th positive integer unused so far.
A permutation of the positive integers.
a(n) = 2n - 1 for odd n, a(n) < 2n - 1 otherwise.

			For n=6, the highest odd divisor of n is k = 3. The sequence up to that point is 1, 2, 5, 3, 9. The numbers which are not yet in the sequence (in increasing order) are S = 4, 6, 7, 8, 10, ... and the 3rd of these is 7, which is therefore a(6).

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A119435, A101319, A000265.

Fold[Append[#1, Complement[Range[Max[#1] + (r = #2/2^IntegerExponent[#2, 2])], #1][[r]]] &, {1}, Range[2, 67]]

cp's OEIS Frontend

A100805 Inverse permutation to sequence A101319 (assuming A101319 is a permutation).

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