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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| Problem 117 in Loren Larson's translation of Paul Vaderlind's book.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..101
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FORMULA
| A007953(A005843(a(n))) = A007953(A000290(a(n))). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 01 2007
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MATHEMATICA
| 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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PROG
| (Haskell)
import Data.List (elemIndices)
import Data.Function (on)
a049343 n = a049343_list !! (n-1)
a049343_list = elemIndices 0
$ zipWith ((-) `on` a007953) a005843_list a000290_list
-- Reinhard Zumkeller, Apr 03 2011
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CROSSREFS
| Cf. A058369, A077436 (binary). [Reinhard Zumkeller, Apr 03 2011]
Sequence in context: A138759 A098934 A043307 * A131140 A022114 A041099
Adjacent sequences: A049340 A049341 A049342 * A049344 A049345 A049346
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KEYWORD
| nonn,base,easy,nice
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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