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Search: id:A049343
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| A049343 |
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Numbers n such that 2n and n^2 have same digit sum. |
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+0
1
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| 0, 2, 9, 11, 18, 20, 29, 38, 45, 47, 90, 99, 101, 110, 119, 144, 146, 180, 182, 189, 198, 200, 245, 290, 299, 335, 344, 351, 362, 369, 380, 398, 450, 452, 459, 461, 468, 470, 479, 488, 495, 497, 639, 729, 794, 839, 848, 900, 929, 954, 990, 999
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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An easy way to prove that this sequence is infinite is to observe that it contains all numbers of the form 10^k+1. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 31 2006
For n>0: digital root (A010888) of 2n or n^2 is either 4 or 9. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 01 2007
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REFERENCES
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Problem 117 in Loren Larson's translation of Paul Vaderlind's book.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..101
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FORMULA
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A007953(A005843(a(n))) = A007953(A000290(a(n))). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 01 2007
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MATHEMATICA
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Select[Range[0, 1000], Sum[DigitCount[2# ][[i]]*i, {i, 1, 9}] == Sum[DigitCount[ #^2][[i]]*i, {i, 1, 9}] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 31 2006
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CROSSREFS
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Sequence in context: A138759 A098934 A043307 this_sequence A131140 A022114 A041099
Adjacent sequences: A049340 A049341 A049342 this_sequence A049344 A049345 A049346
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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