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A316864
Number of times 3 appears in decimal expansion of n.
9
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
OFFSET
0,34
LINKS
FORMULA
From Robert Israel, Dec 10 2019: (Start)
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)
EXAMPLE
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.
MAPLE
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:
map(f, [$0..100]); # Robert Israel, Dec 10 2019
MATHEMATICA
Array[ DigitCount[#, 10, 3] &, 105, 0]
PROG
(PARI) a(n) = #select(x->x==3, digits(n)); \\ Michel Marcus, Jul 20 2018
KEYWORD
base,easy,nonn
AUTHOR
Robert G. Wilson v, Jul 15 2018
STATUS
approved