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A316864
Number of times 3 appears in decimal expansion of n.
10
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