A114727 -id:A114727 - cp's OEIS frontend

A114728 a(n) is the cycle length corresponding to A114727(n).

2, 3, 3, 18, 21, 21, 3, 3, 138, 156, 156, 52, 3, 3, 84, 84, 84, 28, 84, 84, 84, 84, 28, 12, 84, 28, 84, 28, 28, 84, 12, 3, 4, 3, 1376, 1376, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 406, 7, 406, 58, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Klaus Brockhaus, Dec 29 2005

nonn

Besides 1 for fixed points the following lengths of cycles with elements <= 250000 occur: 2, 3, 4, 6, 7, 12, 18, 21, 28, 52, 54, 58, 84, 138, 156, 162, 406, 618, 1376, 1854, 2544, 3953, 5562, 16686.

			A114727(33) = 792 belongs to the 4-cycle (792,1198,1401,995), so a(33) = 4.

Cf. A114650, A114727.

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))).

Original entry on oeis.org

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

A114726 Fixed points of permutation A114650.

Original entry on oeis.org

1, 4, 11, 30, 79, 218, 589, 1604, 4357, 11850, 32203, 87546, 237963, 646864

Offset: 1

Klaus Brockhaus, Dec 29 2005, Jan 10 2006

nonn

Observation: A001671(n) < a(n) < A001671(n+1) for 1 < n <= 14.

Conjecture: Sequence is infinite and lim n -> infinity a(n+1)/a(n) = e = 2.718281828...

			A114650(11) = 11, so 11 is a term.

Cf. A114650, A114727, A001671.

A114892 a(n) is the cycle length corresponding to A114891(n).

Original entry on oeis.org

2, 2, 3, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 10, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 4, 2

Offset: 1

Klaus Brockhaus, Jan 09 2006

nonn

Besides 3 for the cycle (5,7,6) the following lengths of cycles with elements <= 1500000 occur: 2, 4, 6, 10, 12, 16, 18. The even period lengths appear in a rather regular manner, presumably infinitely often.

			A114727(12) = 32 belongs to the 6-cycle (32,37,36,35,34,33), so a(12) = 6.

Cf. A114861, A114891.

A112664 Lengths of k-cycles (k > 1) of permutation A114650 in order of their first appearance.

Original entry on oeis.org

2, 3, 18, 21, 138, 156, 52, 84, 28, 12, 4, 1376, 406, 7, 58, 2544, 3953, 16686, 5562, 1854, 618, 162, 54, 6, 47256, 11814, 1432, 264, 179, 66, 8

Offset: 1

Klaus Brockhaus, Jan 11 2006

Sequence A114728 without repetition.

			(792,1198,1401,995) is the first 4-cycle of A114650, all of the 32 preceding cycles (cf. A114727) have length 2, 3, 18, 21, 138, 156, 52, 84, 28 or 12 (ten different values), hence a(11) = 4.

Cf. A114650, A114728, A114727.

cp's OEIS Frontend

A114728 a(n) is the cycle length corresponding to A114727(n).

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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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A114726 Fixed points of permutation A114650.

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A114892 a(n) is the cycle length corresponding to A114891(n).

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A112664 Lengths of k-cycles (k > 1) of permutation A114650 in order of their first appearance.

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