|
|
A033493
|
|
Sum of the numbers in the trajectory of n for the 3x+1 problem.
|
|
18
|
|
|
1, 3, 49, 7, 36, 55, 288, 15, 339, 46, 259, 67, 119, 302, 694, 31, 214, 357, 519, 66, 148, 281, 633, 91, 658, 145, 101440, 330, 442, 724, 101104, 63, 841, 248, 540, 393, 535, 557, 2344, 106, 101331, 190, 1338, 325, 497, 679, 100979, 139, 806, 708, 1130, 197
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Given a power of two, the value in this sequence is the next higher Mersenne number, or a(2^m) = 2^(m + 1) - 1. - Alonso del Arte, Apr 10 2009
|
|
LINKS
|
|
|
EXAMPLE
|
a(5) = 36 because the Ulam's conjecture trajectory sequence starting on 5 runs 5, 16, 8, 4, 2, 1 and therefore 5 + 16 + 8 + 4 + 2 + 1 = 36. - Alonso del Arte, Apr 10 2009
|
|
MAPLE
|
a:= proc(n) option remember; n+`if`(n=1, 0,
a(`if`(n::even, n/2, 3*n+1)))
end:
|
|
MATHEMATICA
|
collatz[1] = 1; collatz[n_Integer?OddQ] := 3n + 1; collatz[n_Integer?EvenQ] := n/2; Table[-1 + Plus @@ FixedPointList[collatz, n], {n, 60}] (* Alonso del Arte, Apr 10 2009 *)
|
|
PROG
|
(Haskell)
(Python)
def a(n):
if n==1: return 1
l=[n, ]
while True:
if n%2==0: n//=2
else: n = 3*n + 1
l+=[n, ]
if n<2: break
return sum(l)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected a(16) to 31 to match other powers of 2; removed duplicate value of a(48) = 139 because a(49) = 806 and not 139. - Alonso del Arte, Apr 10 2009
|
|
STATUS
|
approved
|
|
|
|