A381762 Numbers k such that S(k) sets a new record, where S(k) denotes the sum of the reciprocals of odd elements in the Collatz sequence which starts at k.

1, 3, 7, 9, 559, 745, 993

Offset: 1

Author

Barak Manos, Mar 06 2025

Keywords

• nonn
• more

Comments

This sequence is conjectured to be finite.

Crossrefs

Cf. A304174.

Cf. A127789.

Programs

Mathematica

f[n_] := Total[1/Select[NestWhileList[If[OddQ[#], 3*# + 1, #/2] &, n, # > 1 &], OddQ]]; seq[lim_] := Module[{s = {}, fm = 0, f1}, Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, lim}]; s]; seq[1000] (* Amiram Eldar, Mar 06 2025 *)

Python

from fractions import Fraction
def S(n):
    arr = []
    while True:
        n //= (n - (n & (n - 1)))
        arr.append(n)
        if n == 1:
            break
        n = 3 * n + 1
    return sum(Fraction(1, x) for x in arr)
m = 0
for n in range(1, 1000):
    k = S(n)
    if m < k:
        m = k
        print(n)