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A316997
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Number of 1's in the first n digits of the binary expansion of sqrt(n).
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1
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0, 1, 1, 2, 1, 2, 4, 3, 5, 2, 5, 5, 9, 7, 11, 13, 1, 7, 9, 9, 12, 9, 11, 14, 10, 2, 13, 13, 16, 12, 16, 12, 16, 19, 18, 15, 2, 21, 18, 20, 19, 25, 19, 20, 25, 26, 19, 24, 26, 3, 20, 25, 25, 31, 28, 36, 30, 33, 33, 37, 38
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OFFSET
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0,4
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LINKS
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Rainer Rosenthal, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n^2) = A000120(n). - Michel Marcus, Dec 15 2018
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EXAMPLE
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For n = 7 we have sqrt(7) = 2.64575131... with binary expansion 10.1010010.... Of the first 7 digits there are a(7) = 3 digits equal to 1.
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MAPLE
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zaehle := proc(n) local e, p, c, i, z, m; Digits := n+5; e := evalf(sqrt(n)); p := [op(convert(e, binary))]; c := convert(p[1], base, 10); z := 0; m := min(n, nops(c)); for i to m do if c[-i] = 1 then z := z+1; fi; od; return z; end: seq(zaehle(n), n=0..60); # Rainer Rosenthal, Dec 14 2018
a := n -> StringTools:-CountCharacterOccurrences(convert(convert(evalf(sqrt(n), n+5), binary, n), string), "1"): seq(a(n), n=0..60); # Peter Luschny, Dec 15 2018
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MATHEMATICA
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a[n_] := Count[RealDigits[Sqrt[n], 2, n][[1]], 1]; Array[a, 60, 0] (* Amiram Eldar, Dec 14 2018 *)
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PROG
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(PARI) a(n)=my(v=concat(binary(sqrt(n)))); hammingweight(v[1..n]) \\ Hugo Pfoertner, Dec 16 2018
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CROSSREFS
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Cf. A004539, A004547, A004555, A004609, A004569, A004585.
Cf. A000120, A000290.
Sequence in context: A131380 A100461 A302655 * A323465 A124904 A187500
Adjacent sequences: A316994 A316995 A316996 * A316998 A316999 A317000
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KEYWORD
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nonn,easy,base
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AUTHOR
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Rainer Rosenthal, Dec 14 2018
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STATUS
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approved
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