cp's OEIS Frontend

A049074 Ulam's conjecture (steps to return n to 1 after division by 2 and, if needed, multiplication by 3 with 1 added).

%I A049074 #35 Aug 29 2025 11:40:59
%S A049074 8,3,49,7,36,55,288,15,339,46,259,67,119,302,694,31,214,357,519,66,
%T A049074 148,281,633,91,658,145,101440,330,442,724,101104,63,841,248,540,393,
%U A049074 535,557,2344,106,101331,190,1338,325,497,679,100979,139,806,708,1130,197
%N A049074 Ulam's conjecture (steps to return n to 1 after division by 2 and, if needed, multiplication by 3 with 1 added).
%C A049074 Appeared in School Science and Mathematics in 1982.
%H A049074 Enoch Haga, <a href="https://doi.org/10.1111/j.1949-8594.1983.tb10148.x">Problem</a>, School Science and Mathematics, Nov 1983, vol. 83, no 7, page 628.
%H A049074 LaBar, <a href="https://doi.org/10.1111/j.1949-8594.1982.tb10084.x">Problem #3929</a>, School Science and Mathematics, Dec 1982, vol. 82 no 8, page 715.
%e A049074 Beginning at n=1, algorithm produces s+t+a=8.
%e A049074 a(3) = 49 because the trajectory of n=3 is (3, 10, 5, 16, 8, 4, 2, 1) and these numbers sum to 49. - _David Radcliffe_, Aug 28 2025
%o A049074 (Python)
%o A049074 def a(n):
%o A049074     if n==1: return 8
%o A049074     l=[n]
%o A049074     while True:
%o A049074         if n%2==0: n//=2
%o A049074         else: n = 3*n + 1
%o A049074         l.append(n)
%o A049074         if n<2: break
%o A049074     return sum(l)
%o A049074 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Apr 14 2017
%Y A049074 Almost the same as A033493.
%Y A049074 Cf. A049067.
%K A049074 easy,nonn,changed
%O A049074 1,1
%A A049074 _Enoch Haga_