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%I #55 Oct 24 2023 02:19:43
%S 1,3,49,7,36,55,288,15,339,46,259,67,119,302,694,31,214,357,519,66,
%T 148,281,633,91,658,145,101440,330,442,724,101104,63,841,248,540,393,
%U 535,557,2344,106,101331,190,1338,325,497,679,100979,139,806,708,1130,197
%N Sum of the numbers in the trajectory of n for the 3x+1 problem.
%C 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
%C a(n) = sum (A070165(k): 1 <= k <= A006577(n)). - _Reinhard Zumkeller_, Oct 08 2011
%H Reinhard Zumkeller, <a href="/A033493/b033493.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e 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
%p a:= proc(n) option remember; n+`if`(n=1, 0,
%p a(`if`(n::even, n/2, 3*n+1)))
%p end:
%p seq(a(n), n=1..55); # _Alois P. Heinz_, Jan 29 2021
%t 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 *)
%o (Haskell)
%o a033493 = sum . a070165_row -- _Reinhard Zumkeller_, Oct 08 2011
%o (Python)
%o def a(n):
%o if n==1: return 1
%o l=[n, ]
%o while True:
%o if n%2==0: n//=2
%o else: n = 3*n + 1
%o l+=[n, ]
%o if n<2: break
%o return sum(l)
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Apr 14 2017
%Y Apart from initial term, exactly the same as A049074. - _Alonso del Arte_, Apr 10 2009
%Y Cf. A006370.
%K nonn
%O 1,2
%A _Jeff Burch_
%E 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
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