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Search: id:A115026
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| A115026 |
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Limiting value of n under iteration of "sum of the digits raised to the power of the number of digits of n" (A101337). |
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| 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, 1, 370, 9, 1, 1, 370, 370, 370, 370, 370, 370, 370, 370, 370, 4, 370, 1, 370, 370, 370, 370, 1, 370, 370, 370, 370, 370, 370, 370, 370, 370, 160, 370, 370, 370, 370, 370, 370
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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EXAMPLE
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E.g. a(89)=370 since:
89 (2 digits): 8^2 + 9^2 = 145
145 (3 digits): 1^3 + 4^3 + 5^3 = 190
190 (3 digits): 1^3 + 9^3 + 0^3 = 730
730 (3 digits): 7^3 + 3^3 + 0^3 = 370
370 (3 digits): 3^3 + 7^3 + 0^3 = 370...etc
So a(89) = 370 since 370 is a constant value under this series.
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CROSSREFS
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Cf. A101337.
Sequence in context: A007953 A080463 A114570 this_sequence A101337 A135208 A156207
Adjacent sequences: A115023 A115024 A115025 this_sequence A115027 A115028 A115029
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KEYWORD
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nonn
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AUTHOR
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Sergio Pimentel (ferdiego(AT)cox.net), Feb 24 2006
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