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

Author

Santi Spadaro, Oct 19 2001

Keywords

• base
• nonn
• nice
• look

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..9999
• Olivier Gerard, Fractal behavior of this sequence (1). [broken link]

Crossrefs

Cf. A007088, A136399, A136400, A136428.

Programs

Haskell

import Data.Char (digitToInt)
a064770 :: Integer -> Integer
a064770 = read . map (("0111222223" !!) . digitToInt) . show
-- Reinhard Zumkeller, Aug 24 2011

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 *)

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