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%I #12 Jun 08 2022 18:30:12
%S 1,2,3,4,5,6,7,8,9,1,2,5,1,370,370,370,370,370,1,4,5,8,1,4,370,370,
%T 370,1,370,9,1,1,370,370,370,370,370,370,370,370,370,4,370,1,370,370,
%U 370,370,1,370,370,370,370,370,370,370,370,370,160,370,370,370,370,370,370
%N Limiting value of n under iteration of "sum of the digits raised to the power of the number of digits of n" (A101337).
%C Iterate A101337 starting at n until reaching a constant value (like 370) or a cycle (like 160, 217, 352, 160, ...). In the latter case, a(n) takes the smallest value in the cycle (e.g., a(59) = 160). Since k*9^k < 10^k for all k > 34, each number n is guaranteed to yield a smaller number a(n) if n > 10^34, so every number reaches a constant or a cycle under this sequence.
%C Conjecture: no term is greater than 370. - _Harvey P. Dale_, Jun 08 2022
%e a(89)=370 since:
%e 89 (2 digits): 8^2 + 9^2 = 145,
%e 145 (3 digits): 1^3 + 4^3 + 5^3 = 190,
%e 190 (3 digits): 1^3 + 9^3 + 0^3 = 730,
%e 730 (3 digits): 7^3 + 3^3 + 0^3 = 370,
%e 370 (3 digits): 3^3 + 7^3 + 0^3 = 370, etc.
%e So a(89) = 370 since 370 is a fixed point of A101337.
%t Table[Min[FindTransientRepeat[NestList[Total[IntegerDigits[#]^IntegerLength[#]]&,n,20],3][[2]]],{n,70}] (* _Harvey P. Dale_, Jun 08 2022 *)
%Y Cf. A101337.
%K nonn,base
%O 1,2
%A _Sergio Pimentel_, Feb 24 2006
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