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

8, 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

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn
• changed

Comments

Appeared in School Science and Mathematics in 1982.

Examples

			Beginning at n=1, algorithm produces s+t+a=8.
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
		

Links

• Enoch Haga, Problem, School Science and Mathematics, Nov 1983, vol. 83, no 7, page 628.
• LaBar, Problem #3929, School Science and Mathematics, Dec 1982, vol. 82 no 8, page 715.

Crossrefs

Almost the same as A033493.

Cf. A049067.

Programs

Python

def a(n):
    if n==1: return 8
    l=[n]
    while True:
        if n%2==0: n//=2
        else: n = 3*n + 1
        l.append(n)
        if n<2: break
    return sum(l)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Apr 14 2017