Search: id:A115026
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%I A115026
%S A115026 1,2,3,4,5,6,7,8,9,1,2,5,1,370,370,370,370,370,1,4,5,8,1,4,370,370,370,
%T A115026 1,370,9,1,1,370,370,370,370,370,370,370,370,370,4,370,1,370,370,370,
%U A115026 370,1,370,370,370,370,370,370,370,370,370,160,370,370,370,370,370,370
%N A115026 Limiting value of n under iteration of "sum of the digits raised to the 
               power of the number of digits of n" (A101337).
%C A115026 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, then 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.
%e A115026 E.g. a(89)=370 since:
%e A115026 89 (2 digits): 8^2 + 9^2 = 145
%e A115026 145 (3 digits): 1^3 + 4^3 + 5^3 = 190
%e A115026 190 (3 digits): 1^3 + 9^3 + 0^3 = 730
%e A115026 730 (3 digits): 7^3 + 3^3 + 0^3 = 370
%e A115026 370 (3 digits): 3^3 + 7^3 + 0^3 = 370...etc
%e A115026 So a(89) = 370 since 370 is a constant value under this series.
%Y A115026 Cf. A101337.
%Y A115026 Sequence in context: A007953 A080463 A114570 this_sequence A101337 A135208 
               A156207
%Y A115026 Adjacent sequences: A115023 A115024 A115025 this_sequence A115027 A115028 
               A115029
%K A115026 nonn
%O A115026 1,2
%A A115026 Sergio Pimentel (ferdiego(AT)cox.net), Feb 24 2006

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