A222752
Irregular array of odd numbers T(n,k) such that the difference between the number of halving and tripling steps in the Collatz (3x+1) iteration is n.
Original entry on oeis.org
1, 3, 5, 13, 21, 7, 11, 17, 9, 15, 23, 35, 53, 85, 19, 29, 45, 69, 75, 113, 25, 37, 61, 93, 141, 151, 213, 227, 341, 33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453, 43, 65, 67, 99, 101, 149, 163, 241, 245, 267, 369, 373, 401, 403, 565, 605, 853, 909, 1365
Offset: 0
The rows are
{1},
{},
{},
{3, 5},
{},
{13, 21},
{7, 11, 17},
{9, 15, 23, 35, 53, 85},
{19, 29, 45, 69, 75, 113},
{25, 37, 61, 93, 141, 151, 213, 227, 341},
{33, 49, 51, 77, 81, 117, 181, 201, 277, 301, 453}
-
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[{}, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, AppendTo[t[[diff + 2]], n]], {n, 1, 2^(nn - 1), 2}]; t
A222753
Number of odd numbers k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n.
Original entry on oeis.org
1, 0, 0, 2, 0, 2, 3, 6, 6, 9, 11, 19, 28, 43, 66, 98, 145, 219, 327, 474, 744, 1125, 1673, 2481, 3723, 5600, 8415, 12630, 18863, 28395, 42620, 63907
Offset: 0
-
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, t[[diff + 2]]++], {n, 1, 2^(nn - 1), 2}]; t
A222755
Greatest odd number k such that difference between halving and tripling steps in Collatz (3x+1) trajectory of k is n, or 0 if there is no such k.
Original entry on oeis.org
1, 0, 0, 5, 0, 21, 17, 85, 113, 341, 453, 1365, 1813, 5461, 7281, 21845, 29125, 87381, 116501, 349525, 466033, 1398101, 1864133, 5592405, 7456533, 22369621, 29826161, 89478485, 119304645, 357913941, 477218581, 1431655765
Offset: 0
-
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 15; t = Table[0, {nn}]; Do[c = Collatz[n]; e = Select[c, EvenQ]; diff = 2*Length[e] - Length[c]; If[diff < nn - 1, t[[diff + 2]] = n], {n, 1, 2^(nn - 1), 2}]; t
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