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A077436
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Let B(n) be the sum of binary digits of n. This sequence contains n such that B(n) = B(n^2).
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29
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0, 1, 2, 3, 4, 6, 7, 8, 12, 14, 15, 16, 24, 28, 30, 31, 32, 48, 56, 60, 62, 63, 64, 79, 91, 96, 112, 120, 124, 126, 127, 128, 157, 158, 159, 182, 183, 187, 192, 224, 240, 248, 252, 254, 255, 256, 279, 287, 314, 316, 317, 318, 319, 351, 364, 365, 366, 374, 375, 379, 384
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OFFSET
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1,3
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COMMENTS
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Hare, Laishram, & Stoll show that this sequence contains infinitely many odd numbers. In particular for each k in {12, 13, 16, 17, 18, 19, 20, ...} there are infinitely many terms in this sequence with binary digit sum k. - Charles R Greathouse IV, Aug 25 2015
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LINKS
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FORMULA
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EXAMPLE
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The element 79 belongs to the sequence because 79=(1001111) and 79^2=(1100001100001), so B(79)=B(79^2)
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MAPLE
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select(t -> convert(convert(t, base, 2), `+`) = convert(convert(t^2, base, 2), `+`), [$0..1000]); # Robert Israel, Aug 27 2015
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MATHEMATICA
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t={}; Do[If[DigitCount[n, 2, 1] == DigitCount[n^2, 2, 1], AppendTo[t, n]], {n, 0, 364}]; t
f[n_] := Total@ IntegerDigits[n, 2]; Select[Range[0, 384], f@ # == f[#^2] &] (* Michael De Vlieger, Aug 27 2015 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
import Data.Function (on)
a077436 n = a077436_list !! (n-1)
a077436_list = elemIndices 0
$ zipWith ((-) `on` a000120) [0..] a000290_list
(Magma) [n: n in [0..400] | &+Intseq(n, 2) eq &+Intseq(n^2, 2)]; // Vincenzo Librandi, Aug 30 2015
(Python)
def ok(n): return bin(n).count('1') == bin(n**2).count('1')
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CROSSREFS
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Cf. A211676 (number of n-bit numbers in this sequence).
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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