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

1,1

Links

Table of n, a(n) for n=1..51.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A339842 A068529 A096059 * A246328 A065772 A305755

Adjacent sequences: A326739 A326740 A326741 * A326743 A326744 A326745

Keyword

nonn,base,easy

Author

Martin Renner, Jul 22 2019

Status

approved