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%I #39 Feb 16 2022 23:59:55
%S 0,2,9,11,18,20,29,38,45,47,90,99,101,110,119,144,146,180,182,189,198,
%T 200,245,290,299,335,344,351,362,369,380,398,450,452,459,461,468,470,
%U 479,488,495,497,639,729,794,839,848,900,929,954,990,999
%N Numbers m such that 2m and m^2 have same digit sum.
%C 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_, Mar 31 2006
%C For n>0: digital root (A010888) of 2n or n^2 is either 4 or 9. - _Reinhard Zumkeller_, Oct 01 2007
%D Problem 117 in Loren Larson's translation of Paul Vaderlind's book.
%H Reinhard Zumkeller and Harvey P. Dale, <a href="/A049343/b049343.txt">Table of n, a(n) for n = 1..1000</a> (first 101 terms from Zumkeller)
%F A007953(A005843(a(n))) = A007953(A000290(a(n))). - _Reinhard Zumkeller_, Oct 01 2007
%t Select[Range[0, 1000], Sum[DigitCount[2# ][[i]]*i, {i, 1, 9}] == Sum[DigitCount[ #^2][[i]]*i, {i, 1, 9}] &] (* _Stefan Steinerberger_, Mar 31 2006 *)
%t Select[Range[0,1000],Total[IntegerDigits[2#]]==Total[ IntegerDigits[ #^2]]&] (* _Harvey P. Dale_, Sep 25 2012 *)
%o (Haskell)
%o import Data.List (elemIndices)
%o import Data.Function (on)
%o a049343 n = a049343_list !! (n-1)
%o a049343_list = elemIndices 0
%o $ zipWith ((-) `on` a007953) a005843_list a000290_list
%o -- _Reinhard Zumkeller_, Apr 03 2011
%o (Magma) [n: n in [0..1000] | &+Intseq(2*n) eq &+Intseq(n^2)]; // _Vincenzo Librandi_, Nov 17 2015
%Y Cf. A058369, A077436 (binary). - _Reinhard Zumkeller_, Apr 03 2011
%K nonn,base,easy,nice,look
%O 1,2
%A _R. K. Guy_
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