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

Author

N. Bradley Fox, Nathan Fox, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024

Keywords

• nonn
• base

Examples

			21 is the 4th elated number and iterating the map A376270 yields 10 then 1, so a(4)=2.
		

Links

• Nathan Fox, Table of n, a(n) for n = 1..7832
• N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.

Crossrefs

Cf. A376270, A376272.

A090425 is the analog for happy numbers, with a different convention used.

Programs

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