[seqfan] Pseudo-Altruistic Number Search

[Hans Havermann]

Back on February 17, Eric Angelini asked Sequence-Fanatics about  
extending the narcissistic-number (A005188) algorithm (raising every  
digit to the power of the number's length and summing) to iterations  
greater than 1. Based on this idea, I submitted on March 4 a (base-10)  
pseudo-altruistic number-sequence: A157714. I have since computed 50  
pseudo-altruistic number cycles, organized by period, here:

http://chesswanks.com/txt/PAN(obp).txt

There is, necessarily, some overlap with the concept of recurring  
digital invariants, on which I will not dwell. Barring errors in  
programming-logic, my list is complete to 10^36. The argument that  
limits the number of narcissistic numbers should also make pseudo- 
altruistic numbers finite. (A 61-digit number iterates to, at most, a  
60-digit number.)

I'm at the end of what I can reasonably expect on my six-year-old  
computer with only a modicum of programming skills. If anyone has the  
time and inclination, they might find it an interesting exercise to  
verify my results and/or extend them beyond.