A358439 -id:A358439 - cp's OEIS frontend

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

N. J. A. Sloane, Oct 07 2001

Assumes that 4 is represented without a hole.

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

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

Cf. A064529, A064530. Equals A064531 - 1.

Cf. A358439 (sum by number of digits).

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 *)

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

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

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

More terms from Matthew Conroy, Oct 09 2001

A359271 Number of odd digits necessary to write all nonnegative n-digit integers.

Original entry on oeis.org

5, 95, 1400, 18500, 230000, 2750000, 32000000, 365000000, 4100000000, 45500000000, 500000000000, 5450000000000, 59000000000000, 635000000000000, 6800000000000000, 72500000000000000, 770000000000000000, 8150000000000000000

Offset: 1

Bernard Schott, Dec 23 2022

			To write the integers from 10 up to 99, each of the digits 1, 3, 5, 7 and 9, must be used 19 times, hence a(2) = 19*5 = 95.

Index entries for linear recurrences with constant coefficients, signature (20,-100).

Cf. A113119, A196564, A279766, A358439.

Maple
```
seq(5 * (9*n+1) * 10^(n-2), n=1..18);
```

a[n_] := 5*(9*n + 1)*10^(n - 2); Array[a, 20] (* Amiram Eldar, Dec 23 2022 *)

a(n) = 5 * (9*n+1) * 10^(n-2).
a(n) = A279766(10^n-1) - A279766(10^(n-1)-1).
a(n) = A113119(n) - A358439(n).
From Stefano Spezia, Dec 24 2022: (Start)
O.g.f.: 5*x*(1 - x)/(1 - 10*x)^2.
E.g.f.: (exp(10*x)*(1 + 90*x) - 1)/20. (End)

cp's OEIS Frontend

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

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