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

Author

Leroy Quet, Dec 21 2005

Keywords

• easy
• nonn

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

Examples

			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.

Extensions

More terms from Klaus Brockhaus, Dec 25 2005