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Search: id:A046017
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| A046017 |
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Least k > 1 with k = sum of digits of k^n, or 0 if no such k exists. |
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+0
6
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| 2, 9, 8, 7, 28, 18, 18, 46, 54, 82, 98, 108, 20, 91, 107, 133, 80, 172, 80, 90, 90, 90, 234, 252, 140, 306, 305, 90, 305, 396, 170, 388, 170, 387, 378, 388, 414, 468, 449, 250, 432, 280, 461, 280, 360, 360, 350, 370, 270, 685, 360, 625, 648, 370, 677, 684, 370, 667, 370, 694, 440, 855, 827, 430, 818
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First non-occurrence happens with exponent 105. There is no x such that sum-of-digits{x^105}=x (x>1).
a(13)=20: 20^13=81920000000000000, 8+1+9+2=20; a(17)=80: 80^17=225179981368524800000000000000000, 2+2+5+1+7+9+9+8+1+3+6+8+5+2+4+8 = 80.
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REFERENCES
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Joe Roberts, "Lure of the Integers", The Mathematical Association of America, 1992, p. 172.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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a(3) = 8 since 8^3 = 512 and 5+1+2 = 8; a(5) = 28 because 28 is least number > 1 with 28^5 = 17210368, 1+7+2+1+0+3+6+8 = 28. 53^7 = 1174711139837 -> 1+1+7+4+7+1+1+1+3+9+8+3+7 = 53.
a(10) = 82 because 82^10 = 13744803133596058624 and 1 + 3 + 7 + 4 + 4 + 8 + 0 + 3 + 1 + 3 + 3 + 5 + 9 + 6 + 0 + 5 + 8 + 6 + 2 + 4 = 82.
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CROSSREFS
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Cf. A046459, A046000, A046471, A061211.
Cf. A133509 (n for which a(n)=0), A152147 (table of k for each n)
Sequence in context: A077601 A090930 A151927 this_sequence A155909 A069815 A162954
Adjacent sequences: A046014 A046015 A046016 this_sequence A046018 A046019 A046020
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KEYWORD
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base,nonn,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Additional comments from Patrick De Geest, Aug 15 1998. More terms from Asher Natan Auel (auela(AT)reed.edu), Jun 01 2000
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