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

1,2

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.

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

Prog

(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

Crossrefs

Cf. A376270, A376273.

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

Sequence in context: A159839 A129075 A095918 * A191969 A018785 A176762

Adjacent sequences: A376269 A376270 A376271 * A376273 A376274 A376275

Keyword

nonn,base

Author

Michel Marcus, Sep 18 2024

Status

approved