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

Author

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

Keywords

• nonn
• base

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

Crossrefs

Cf. A003132, A007770, A376270, A376272.

Programs

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