A113701 -id:A113701 - cp's OEIS frontend

A113700 Members of 2-cycles of permutation A111273.

2, 3, 50, 75, 122, 174, 183, 194, 203, 291, 338, 410, 507, 615, 722, 794, 842, 914, 1058, 1082, 1083, 1154, 1182, 1191, 1202, 1263, 1346, 1371, 1379, 1442, 1562, 1572, 1587, 1623, 1682, 1703, 1731, 1778, 1803, 1922, 2018, 2019, 2066, 2163, 2343, 2354, 2426

Offset: 1

Klaus Brockhaus, Nov 08 2005

nonn

Trajectory of n under map k -> A111273(k) is periodic with period length 2.
n = A111273(A111273(n)) and n <> A111273(n).
Apparently A111273 has infinitely many 2-cycles.

			A111273(122) = 183 and A111273(183) = 122, hence 122 and 183 are in the
sequence.

Cf. A111273, A113659, A113701.

A113702 Trajectory of 10 under map k -> A111273(k).

Original entry on oeis.org

10, 11, 22, 23, 12, 13, 91, 161, 189, 285, 429, 473, 869, 957, 1437, 2157, 3237, 4857, 7287, 4164, 3470, 4511, 2256, 1464, 1172, 782, 783, 392, 294, 413, 531, 342, 343, 172, 173, 519, 346, 347, 694, 1735, 1388, 926, 927, 464, 248, 166, 167, 84, 70, 71, 36, 37

Offset: 0

Klaus Brockhaus, Nov 08 2005

nonn

10 is the smallest number that is not member of a k-cycle with k <=13 of permutation A111273.
Conjecture: Sequence is not periodic.
For the retrograde trajectory of 10 see A113703.

Robert Israel, Table of n, a(n) for n = 0..81

Cf. A111273, A113659, A113700, A113701, A113703.

# assuming A111273 is a list, Vector or table
a113702[0]:= 10:
for i from 1 do
  t:= traperror(A111273[a113702[i-1]]);
if not t::integer then break fi;
  a113702[i]:=t
od:
seq(a113702[j],j=0..i-1); # Robert Israel, Jan 16 2019

A113703 Retrograde trajectory of 10 under map k -> A111273(k).

Original entry on oeis.org

10, 19, 18, 27, 26, 39, 38, 56, 111, 74, 147, 146, 219, 218, 435, 290, 579, 578, 867, 866, 1299, 1298, 1947, 1121, 589, 341, 186, 371, 265, 105, 69, 45, 44, 55, 54, 80, 159, 53, 52, 103, 102, 152, 208, 415, 414, 459, 458, 915, 365, 145, 115, 114, 132, 176, 351, 350

Offset: 0

Klaus Brockhaus, Nov 08 2005

nonn

Also trajectory of 10 under map k -> A113658(k).
Conjecture: Sequence is not periodic.
For the trajectory of 10 under map k -> A111273(k) see A113702.

Cf. A111273, A113658, A113659, A113700, A113701, A113702.

cp's OEIS Frontend

A113700 Members of 2-cycles of permutation A111273.

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A113702 Trajectory of 10 under map k -> A111273(k).

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A113703 Retrograde trajectory of 10 under map k -> A111273(k).

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