[seqfan] Fixpoints of the powertrain map (A133500) in different bases?

[Georg.Fischer]

The recent article in the German "Spektrum"
magazine led me to <https://oeis.org/A135385>
"Fixed points of the map m -> powertrain(m)" (2007),
and I was astonished and puzzled by the terms
2592, 24547284284866560000000000 and the comments:
- Probably there are no other terms.
- There are no other terms below 10^100.

In an attempt to get some additional idea I used a
brute-force program which calculates the powertrain map
(A133500) not only in decimal, but *in different bases*.
It's not fast, so I only ran it up to n <= 30000.
It shows the following non-trivial (> base) fixpoints:

- none for base 2, 3, 4, 5
- 16(10)    -> ... 16(10)=24(6)
- none for 7
- 27(10)    -> ... 27(10)=33(8)
   230(10)   -> ... 486(10)=746(8)->14406(10)=34106(8)->486(10)=746(8)
   3196(10)  -> ... 14406(10)=34106(8)->486(10)=746(8)
                    ->14406(10)=34106(8)
   [base 8 leads to a *cycle with two elements*; checked up to n=500000]
- 5344(10)  -> ... 24586240(10)=51232874(9)
- 129(10)   -> ... 7996018508417728512(10)=372b9a830000000000(12)
   486(10)   -> ... 486(10)=346(12)
   509(10)   -> ... 39366(10)=1a946(12)
   1082(10)  -> ... 29282(10)=14b42(12)
   9895(10)  -> ... 819200000000(10)=11292450a0a8(12)
- none for 13, 14, 15
- 25143(10) -> ... 78732(10)=1338c(16)
- 29652(10) -> ... 10000(10)=20a4(17)
- 24679(10) -> ... 768(10)=26c(18)
- 1604(10)  -> ... 524288(10)=40862(19)
- 124(10)   -> ... 1296(10)=34g(20)
- 937(10)   -> ... 1024(10)=26g(21)
- 27082(10) -> ... 2048(10)=452(22)
- none for 23
- 4116(10)  -> ... 4116(10)=73c(24)
- none for 25
- 85(10)    -> ... 2187(10)=363(26)
- none for 27, 28

Now my questions:
- Are such fixpoint lists (especially for base 8, 12)
   worth to become OEIS sequences?
- Should I try to write a faster program, and
   examine higher ranges?
- Obviously a much more efficient program or argument
   was used for the check <= 10^100 mentioned in A135385?
   Which one?

Regards - Georg