A326742 Numbers which converge to 9 under repeated application of the powertrain map of A133500.

9, 25, 32, 52, 91, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 228, 234, 242, 251, 279, 295, 309, 313, 321, 337, 377, 409, 418, 422, 509, 515, 521, 539, 544, 609, 709, 809, 814, 835, 909, 911, 965, 1025, 1032, 1052, 1091, 1125, 1132, 1152, 1191

Offset: 1

Author

Martin Renner, Jul 22 2019

Keywords

• nonn
• base
• easy

Examples

			25 -> 2^5 = 32 -> 3^2 = 9.
		

Crossrefs

Cf. A133500, A133501, A135384, A135385, A309385, A326733, A326734, A326735, A326736, A326737, A326738, A326739, A326740, A326741.

Programs

Python

def powertrain(n):
    p, s = 1, str(n)
    if len(s)%2 == 1: s += '1'
    for b, e in zip(s[0::2], s[1::2]): p *= int(b)**int(e)
    return p
def aupto(limit, target=0):
    alst = []
    for n in range(1, limit+1):
        m, ptm = n, powertrain(n)
        while m != ptm: m, ptm = ptm, powertrain(ptm)
        if m == target: alst.append(n)
    return alst
print(aupto(1191, target=9)) # Michael S. Branicky, Sep 25 2021