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

1,2

Comments

This sequence is conjectured to be finite.

Links

Table of n, a(n) for n=1..7.

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 *)

Prog

(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)

Crossrefs

Cf. A304174.

Cf. A127789.

Sequence in context: A118559 A189244 A127789 * A112105 A065501 A144385

Adjacent sequences: A381759 A381760 A381761 * A381763 A381764 A381765

Keyword

nonn,more

Author

Barak Manos, Mar 06 2025

Status

approved