A064770 Replace each digit of n with the floor of its square root.

0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 20, 21, 21, 21, 22, 22, 22, 22, 22, 23, 20, 21, 21, 21, 22, 22, 22, 22, 22, 23, 20, 21, 21, 21, 22, 22, 22, 22, 22, 23

Offset

0,5

Comments

The graph of this sequence is fractal-like.

a(A007088(n))=A007088(n); a(A136399(n))<>A136399(n); a(a(n))=A136400(n); a(A136400(n))=A136400(n); A136428(n)=a(n+1)-a(n). - Reinhard Zumkeller, Dec 30 2007

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..9999

Olivier Gerard, Fractal behavior of this sequence (1). [broken link]

Example

26 -> [1.414...][2.449...] -> 12, so a(26) = 12.

Maple

a:= n-> (l-> add(([0, 1$3, 2$5, 3][l[i]+1])*10^i,
         i=1..nops(l))/10)(convert(n, base, 10)):
seq(a(n), n=0..69);  # Alois P. Heinz, Oct 19 2024

Mathematica

Table[ FromDigits[ Floor[ Sqrt[ IntegerDigits[ n]]]], {n, 0, 100} ]
With[{dg=Table[n->Floor[Sqrt[n]], {n, 0, 9}]}, Table[FromDigits[ IntegerDigits[ k]/.dg], {k, 0, 100}]] (* Harvey P. Dale, Oct 23 2020 *)

Prog

(Haskell)
import Data.Char (digitToInt)
a064770 :: Integer -> Integer
a064770 = read . map (("0111222223" !!) . digitToInt) . show
-- Reinhard Zumkeller, Aug 24 2011
(PARI) a(n) = fromdigits(apply(sqrtint, digits(n))); \\ Michel Marcus, Nov 12 2023
(Python)
def A064770(n): return int(''.join(map(lambda x:'0111222223'[int(x)], str(n)))) # Chai Wah Wu, Oct 19 2024

Crossrefs

Cf. A007088, A136399, A136400, A136428.

Sequence in context: A114968 A079629 A029116 * A322073 A332201 A060467

Adjacent sequences: A064767 A064768 A064769 * A064771 A064772 A064773

Keyword

base,nonn,nice,look

Author

Santi Spadaro, Oct 19 2001

Status

approved