A264969 -id:A264969 - cp's OEIS frontend

A264965 Permutation of nonnegative integers: a(n) = A263273(A057889(n)).

0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 13, 12, 19, 22, 21, 16, 25, 18, 17, 20, 15, 26, 55, 24, 11, 14, 27, 28, 23, 30, 37, 64, 57, 46, 43, 36, 67, 70, 33, 40, 31, 66, 79, 52, 63, 38, 47, 48, 73, 58, 75, 76, 49, 54, 65, 56, 39, 34, 29, 60, 61, 74, 45, 32, 59, 42, 145, 68, 81, 226, 193, 72, 35, 82, 219, 100, 217, 174, 121, 80, 69

Offset: 0

Antti Karttunen, Dec 05 2015

Perform an adjusted reverse of n in base 2, followed by another adjusted reverse in base 3. "Adjusted reverse" here means the digit-reversing operation in which the tail of trailing zeros (in the base in question) is fixed, while the portion from the most significant digit to the least significant nonzero digit is reversed.

What percentage of the cycles are finite? (See the scatter-plot and A264969, also A264972, A264973.)

Antti Karttunen, Table of n, a(n) for n = 0..10000
Indranil Ghosh, Python program to generate the sequence

Inverse: A264966.
Cf. A000035, A057889, A263273, A264969, A264972, A264973.
Cf. also A264967, A264968.

(define (A264965 n) (A263273 (A057889 n)))

a(n) = A263273(A057889(n)).
Other identities. For all n >= 0:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

A264972 Trajectory of 262 under repeated application of the permutation A264965: a(0) = 262; for n >= 1, a(n) = A264965(a(n-1)).

Original entry on oeis.org

262, 670, 1450, 1690, 2158, 4246, 19522, 18410, 34678, 36926, 118882, 146998, 290566, 377966, 240038, 381466, 407054, 178898, 147146, 149714, 159458, 149378, 129242, 117958, 157822, 350014, 489878, 180770, 155930, 395686, 510386, 292426, 514294, 503114, 264490, 435670, 482882, 311674, 452774, 353570, 323374, 369638, 321926, 293726

Offset: 0

Antti Karttunen, Dec 06 2015

The trajectory is probably infinite, not periodic.

			a(0) = 262 by definition. Its binary representation is A007088(262) = 100000110. When we reverse the significant prefix (i.e., leave the trailing zeros where they are), we get 386 (A007088(386) = 110000010). 386's ternary representation is A007089(386) = 112022. Reversing the significant prefix (now the whole expansion because no trailing zeros present), we get 220211 (= A007089(670)), thus a(1) = 670.

Antti Karttunen, Table of n, a(n) for n = 0..1000

Cf. A007088, A007089, A264965, A264969, A264973.

a(0) = 262; for n >= 1, a(n) = A264965(a(n-1)).

A264973 Trajectory of 262 under permutation A264966: a(0) = 262; for n >= 1, a(n) = A264966(a(n-1)).

Original entry on oeis.org

262, 338, 850, 1058, 1238, 1838, 1786, 734, 1622, 1594, 710, 554, 818, 1118, 1574, 2014, 1834, 1306, 742, 1922, 1270, 838, 1018, 718, 334, 290, 802, 622, 322, 494, 650, 478, 266, 946, 550, 274, 458, 922, 766, 790, 1778, 1054, 826, 1418, 1358, 1982, 1606, 1954, 614, 674, 794, 1478, 1702, 986, 1526, 1870, 1714, 1090, 598, 298, 386, 970, 1370

Offset: 0

Antti Karttunen, Dec 06 2015

The trajectory is probably infinite, not periodic.

			a(0) = 262 by definition. Its base-3 representation is A007089(262) = 100201. Reversing the significant prefix (in this case the whole expansion because no trailing zeros present), we get 102001 (= A007089(298)). Base-2 representation of 298 is 100101010 (= A007088(298)). Reversing its significant prefix, we get 101010010 (= A007088(338)), thus a(1) = 338.

Antti Karttunen, Table of n, a(n) for n = 0..1000

Cf. A007088, A007089, A264966, A264969, A264972.

a(0) = 262; for n >= 1, a(n) = A264966(a(n-1)).

cp's OEIS Frontend

A264965 Permutation of nonnegative integers: a(n) = A263273(A057889(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A264972 Trajectory of 262 under repeated application of the permutation A264965: a(0) = 262; for n >= 1, a(n) = A264965(a(n-1)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A264973 Trajectory of 262 under permutation A264966: a(0) = 262; for n >= 1, a(n) = A264966(a(n-1)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula