A376272 Elated numbers: numbers whose trajectory under iteration of the A376270 map includes 1.

1, 10, 13, 21, 43, 51, 67, 77, 88, 92, 97, 100, 103, 117, 124, 130, 142, 155, 171, 201, 210, 226, 237, 256, 262, 265, 273, 319, 322, 337, 356, 365, 373, 391, 403, 430, 438, 483, 501, 510, 514, 541, 556, 565, 579, 588, 597, 607, 616, 639, 661, 668, 670, 686, 693, 699, 707, 717, 724, 742, 746

Offset: 1

Author

Michel Marcus, Sep 18 2024

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.

Crossrefs

Cf. A376270, A376273.

b-elated numbers: A000027 (2), A376272 (10).

Programs

Maple

b:= proc(n) b(n):= (l-> l[-1]*add(i^2, i=l))(convert(n, base, 10)) end:
q:= proc(n) option remember; local k, s; k, s:= n, {};
      while not (k=1 or k in s) do s, k:= {s[], k}, b(k) od: is(k=1)
    end:
select(q, [$1..1000])[];  # Alois P. Heinz, Sep 18 2024

PARI

f(n) = if (n, my(d=digits(n)); d[1]*norml2(d), 0); \\ A376270
isok(n) = my(list=List()); while(1, my(m=f(n)); if (m==1, return(1)); if (#select(x->(x==m), Vec(list)), return(0)); listput(list, m); n=m); 0;

Python

def f(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)
def ok(n):
    if n == 1: return True
    traj = {n}
    while (n:=f(n)) not in traj: traj.add(n)
    return 1 in traj
print([k for k in range(750) if ok(k)]) # Michael S. Branicky, Sep 18 2024