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

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

Author

Robert G. Wilson v, Jul 15 2018

Keywords

• base
• easy
• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A043501, A043502, A043503, A043504.

Cf. A055641, A268643, A316864, A316865, A316866, A316867, A316868, A316869, A102683.

Programs

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]

PARI

a(n) = #select(x->x==3, digits(n)); \\ Michel Marcus, Jul 20 2018

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)