A316997 Number of 1's in the first n digits of the binary expansion of sqrt(n).

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

Offset

0,4

Links

Rainer Rosenthal, Table of n, a(n) for n = 0..1000

Formula

a(n^2) = A000120(n). - Michel Marcus, Dec 15 2018

Example

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.

Maple

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

Mathematica

a[n_] := Count[RealDigits[Sqrt[n], 2, n][[1]], 1]; Array[a, 60, 0] (* Amiram Eldar, Dec 14 2018 *)

Prog

(PARI) a(n)=my(v=concat(binary(sqrt(n)))); hammingweight(v[1..n]) \\ Hugo Pfoertner, Dec 16 2018

Crossrefs

Cf. A004539, A004547, A004555, A004609, A004569, A004585.

Cf. A000120, A000290.

Sequence in context: A131380 A100461 A302655 * A323465 A364780 A124904

Adjacent sequences: A316994 A316995 A316996 * A316998 A316999 A317000

Keyword

nonn,easy,base

Author

Rainer Rosenthal, Dec 14 2018

Status

approved