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
Examples
8 has two holes so a(8) = 2.
Links
- Indranil Ghosh, Table of n, a(n) for n = 0..50000
Programs
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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
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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
Comments