|
Search: id:A078420
|
|
|
| A078420 |
|
Numbers n such that h(n) = 3 h(n-1) where h(n) is the length of the sequence {n, f(n), f(f(n)), ...., 1} in the Collatz (or 3x + 1) problem. (The earliest "1" is meant.) |
|
+0
3
|
|
| 105, 548, 683, 1508, 3652, 4278, 4295, 8145, 8150, 9417, 9419, 18247, 18287, 18370, 18433, 18586, 18695, 18706, 18742, 18945, 22024, 22140, 22311, 22324, 22708, 22714, 25336, 25681, 25771, 25777, 25785, 25814, 44545, 44593, 46505, 46847
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Recall that f(n) = n/2 if n is even; = 3n + 1 if n is odd.
|
|
EXAMPLE
|
n, f(n), f(f(n)), ...., 1 for n = 105, 104, respectively, are: 105, 316, 158, 79, 238, 119, 358, 179, 538, 269, 808, 404, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1; 104, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, of lengths 39 = 3 x 13 and 13, respectively. Hence 105 belongs to the sequence.
|
|
MATHEMATICA
|
f[n_] := If[EvenQ[n], n/2, 3n+1]; h[n_] := Module[{a, i}, i=n; a=1; While[i>1, a++; i=f[i]]; a]; Select[Range[2, 47000], 3h[ #-1]==h[ # ]&]
|
|
CROSSREFS
|
Cf. A078418, A078419.
Sequence in context: A165060 A165069 A143041 this_sequence A152826 A133767 A166816
Adjacent sequences: A078417 A078418 A078419 this_sequence A078421 A078422 A078423
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 29 2002
|
|
EXTENSIONS
|
Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 30 2002
|
|
|
Search completed in 0.002 seconds
|
