A377089 Numbers that are both happy (A007770) and elated (A376272).

1, 10, 13, 97, 100, 103, 130, 226, 262, 319, 356, 365, 391, 556, 565, 907, 970, 1000, 1003, 1030, 1122, 1177, 1188, 1212, 1221, 1222, 1277, 1300, 1339, 1393, 1448, 1478, 1484, 1487, 1557, 1575, 1717, 1727, 1748, 1755, 1771, 1772, 1784, 1818, 1844, 1847, 1874

Offset

1,2

Comments

Every power of 10 is in this sequence, as both the sum of squared digits map (A003132) and the map A376270 map powers of 10 to 1.

Links

Nathan Fox, Table of n, a(n) for n = 1..12205

Prog

(Python)
def ssd(n): return sum(int(d)**2 for d in str(n))
def f(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)
def happy(n):
    if n == 1: return True
    s = list(map(int, str(n)))
    while n not in [1, 4]: n = ssd(n) # iterate until fixed point or cycle
    return n == 1
def elated(n):
    if n == 1: return True
    traj = {n}
    while (n:=f(n)) not in traj: traj.add(n)
    return 1 in traj
def ok(n): return happy(n) and elated(n)
print([k for k in range(1, 2001) if ok(k)]) # Michael S. Branicky, Oct 16 2024

Crossrefs

Cf. A003132, A007770, A376270, A376272.

Sequence in context: A384377 A154142 A219804 * A108761 A164766 A219455

Adjacent sequences: A377086 A377087 A377088 * A377090 A377091 A377092

Keyword

nonn,base

Author

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

Status

approved