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A377083 Number of iterations required for elated number A376272(n) to converge to 1.

%I A377083 #10 Oct 16 2024 20:53:43
%S A377083 0,1,2,2,2,3,4,7,4,9,5,1,2,4,3,2,3,4,4,2,2,5,4,3,5,3,4,5,4,3,3,3,3,5,
%T A377083 2,2,4,4,3,3,3,3,3,3,7,9,7,4,5,9,5,6,4,6,9,4,7,10,5,5,8,10,8,6,8,8,7,
%U A377083 10,6,4,5,6,7,6,2,5,7,2,7,4,7,9,5,9,5,5
%N A377083 Number of iterations required for elated number A376272(n) to converge to 1.
%H A377083 Nathan Fox, <a href="/A377083/b377083.txt">Table of n, a(n) for n = 1..7832</a>
%H A377083 N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.
%e A377083 21 is the 4th elated number and iterating the map A376270 yields 10 then 1, so a(4)=2.
%o A377083 (Python)
%o A377083 from itertools import count, islice
%o A377083 def f(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)
%o A377083 def ok_count(n):
%o A377083     if n == 1: return True, 0
%o A377083     traj, c = {n}, 0
%o A377083     while (n:=f(n)) not in traj: traj.add(n); c += 1
%o A377083     return 1 in traj, c
%o A377083 def agen(): # generator of terms
%o A377083     for n in count(1):
%o A377083         elated, iterations = ok_count(n)
%o A377083         if elated: yield iterations
%o A377083 print(list(islice(agen(), 90))) # _Michael S. Branicky_, Oct 16 2024
%Y A377083 Cf. A376270, A376272.
%Y A377083 A090425 is the analog for happy numbers, with a different convention used.
%K A377083 nonn,base
%O A377083 1,3
%A A377083 N. Bradley Fox, _Nathan Fox_, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024