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A377083
Number of iterations required for elated number A376272(n) to converge to 1.
1
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, 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, 10, 6, 4, 5, 6, 7, 6, 2, 5, 7, 2, 7, 4, 7, 9, 5, 9, 5, 5
OFFSET
1,3
LINKS
N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.
EXAMPLE
21 is the 4th elated number and iterating the map A376270 yields 10 then 1, so a(4)=2.
PROG
(Python)
from itertools import count, islice
def f(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)
def ok_count(n):
if n == 1: return True, 0
traj, c = {n}, 0
while (n:=f(n)) not in traj: traj.add(n); c += 1
return 1 in traj, c
def agen(): # generator of terms
for n in count(1):
elated, iterations = ok_count(n)
if elated: yield iterations
print(list(islice(agen(), 90))) # Michael S. Branicky, Oct 16 2024
CROSSREFS
A090425 is the analog for happy numbers, with a different convention used.
Sequence in context: A339711 A048185 A368520 * A095094 A275009 A103894
KEYWORD
nonn,base
AUTHOR
N. Bradley Fox, Nathan Fox, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024
STATUS
approved