A114650 a(1)=1. For n>1, a(n) is smallest positive integer not among the earlier terms of the sequence such that floor(log(a(n))) does not equal floor(log(a(n-1))).

1, 3, 2, 4, 8, 5, 9, 6, 10, 7, 11, 21, 12, 22, 13, 23, 14, 24, 15, 25, 16, 26, 17, 27, 18, 28, 19, 29, 20, 30, 55, 31, 56, 32, 57, 33, 58, 34, 59, 35, 60, 36, 61, 37, 62, 38, 63, 39, 64, 40, 65, 41, 66, 42, 67, 43, 68, 44, 69, 45, 70, 46, 71, 47, 72, 48, 73, 49, 74, 50, 75, 51

Offset

1,2

Comments

Sequence is a permutation of the positive integers. (Sequence A114651 is the inverse permutation.)

Apparently this permutation is completely decomposable into (disjoint) cycles of finite length. The number of fixed points (cf. A114726) seems to be infinite, but for each k>1 there are presumably only finitely many cycles of length k (cf. A114727 and A114728). - Klaus Brockhaus, Dec 29 2005

Links

Table of n, a(n) for n=1..72.

Example

Since all positive integers m where floor(log(m)) equals 0 or 1 occur among the first 11 terms of the sequence and since floor(log(a(11))) = 2, then a(12) must be 21 (which is the smallest positive integer m such that floor(log(m)) = 3).

Crossrefs

Cf. A114651, A000195, A001671, A114726, A114727, A114728.

Sequence in context: A231330 A254051 A082228 * A170949 A276953 A276943

Adjacent sequences: A114647 A114648 A114649 * A114651 A114652 A114653

Keyword

easy,nonn

Author

Leroy Quet, Dec 21 2005

Extensions

More terms from Klaus Brockhaus, Dec 25 2005

Status

approved