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

1,3

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.

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

Cf. A376270, A376272.

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

Sequence in context: A339711 A048185 A368520 * A095094 A275009 A103894

Adjacent sequences: A377080 A377081 A377082 * A377084 A377085 A377086

Keyword

nonn,base

Author

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

Status

approved