A064532 Total number of holes in decimal expansion of the number n, assuming 4 has no hole.

1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 2, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 3, 2, 2, 2, 2, 2, 3, 2, 4, 3, 2, 1, 1, 1, 1, 1, 2, 1, 3, 2, 2, 1, 1, 1, 1

Offset: 0

Author

N. J. A. Sloane, Oct 07 2001

Keywords

• nonn
• easy
• base

Comments

Assumes that 4 is represented without a hole.

Examples

			8 has two holes so a(8) = 2.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..50000

Crossrefs

Cf. A064529, A064530. Equals A064531 - 1.

Cf. A358439 (sum by number of digits).

Programs

Mathematica

a[n_ /; 0 <= n <= 9] := a[n] = {1, 0, 0, 0, 0, 0, 1, 0, 2, 1}[[n + 1]]; a[n_] := Total[a[#] + 1 &  /@ (id = IntegerDigits[n])] - Length[id];  Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Nov 22 2013 *)
Table[DigitCount[x].{0, 0, 0, 0, 0, 1, 0, 2, 1, 1}, {x, 0, 104}] (* Michael De Vlieger, Feb 02 2017, after Zak Seidov at A064692 *)

PARI

h(n) = [1, 0, 0, 0, 0, 0, 1, 0, 2, 1][n];
a(n) = if (n, my(d=digits(n)); sum(i=1, #d, h(d[i]+1)), 1); \\ Michel Marcus, Nov 11 2022

Python

def A064532(n):
    x=str(n)
    return x.count("0")+x.count("6")+x.count("8")*2+x.count("9") # Indranil Ghosh, Feb 02 2017

Formula

a(10i+j) = a(i) + a(j), etc.

Extensions

More terms from Matthew Conroy, Oct 09 2001