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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.

%I A381762 #19 Mar 15 2025 12:28:00
%S A381762 1,3,7,9,559,745,993
%N 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.
%C A381762 This sequence is conjectured to be finite.
%t A381762 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 *)
%o A381762 (Python)
%o A381762 from fractions import Fraction
%o A381762 def S(n):
%o A381762     arr = []
%o A381762     while True:
%o A381762         n //= (n - (n & (n - 1)))
%o A381762         arr.append(n)
%o A381762         if n == 1:
%o A381762             break
%o A381762         n = 3 * n + 1
%o A381762     return sum(Fraction(1, x) for x in arr)
%o A381762 m = 0
%o A381762 for n in range(1, 1000):
%o A381762     k = S(n)
%o A381762     if m < k:
%o A381762         m = k
%o A381762         print(n)
%Y A381762 Cf. A304174.
%Y A381762 Cf. A127789.
%K A381762 nonn,more
%O A381762 1,2
%A A381762 _Barak Manos_, Mar 06 2025