A114726 -id:A114726 - cp's OEIS frontend

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

Leroy Quet, Dec 21 2005

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

			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).

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

More terms from Klaus Brockhaus, Dec 25 2005

A114727 Numbers that are the least element of a k-cycle (k > 1) of permutation A114650.

Original entry on oeis.org

2, 5, 7, 12, 31, 33, 37, 51, 80, 219, 221, 225, 271, 377, 590, 592, 594, 596, 600, 602, 604, 606, 610, 618, 620, 624, 626, 638, 666, 668, 676, 734, 792, 1024, 1605, 1607, 4358, 4360, 4362, 4364, 4366, 4368, 4370, 4372, 4376, 4378, 4380, 4384, 4386, 4388

Offset: 1

Klaus Brockhaus, Dec 29 2005

nonn

The corresponding cycle lengths are given in A114728.

Elements of 1-cycles (fixed points) are given in A114726.

			(792,1198,1401,995) is a cycle of permutation A114650, so 792 is a term.

Cf. A114650, A114728, A114726.

cp's OEIS Frontend

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))).

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