Search: a043502 -id:a043502
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A316864
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Number of times 3 appears in decimal expansion of n.
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+10
9
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0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
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OFFSET
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0,34
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LINKS
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FORMULA
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a(10*n+3) = a(n)+1, a(10*n+i)=a(i) for i = 0,1,2,4..9.
G.f. g(z) satisfies g(z) = z^3/(1-z^10) + ((1-z^10)/(1-z))*g(z^10). (End)
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EXAMPLE
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a(0) = 0 since the decimal representation of 0 does not contain the digit 3.
a(3) = 1 since 3 appears once in the decimal expansion of 3.
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MAPLE
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f:= proc(n) option remember;
procname(floor(n/10)) + `if`(n mod 10 = 3, 1, 0)
end proc:
for i from 0 to 9 do f(i):= `if`(i=3, 1, 0) od:
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MATHEMATICA
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Array[ DigitCount[#, 10, 3] &, 105, 0]
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PROG
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(PARI) a(n) = #select(x->x==3, digits(n)); \\ Michel Marcus, Jul 20 2018
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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