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

0,34

Links

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

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

Crossrefs

Cf. A043501, A043502, A043503, A043504.

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

Sequence in context: A157746 A349082 A281010 * A037820 A076493 A278907

Adjacent sequences: A316861 A316862 A316863 * A316865 A316866 A316867

Keyword

base,easy,nonn

Author

Robert G. Wilson v, Jul 15 2018

Status

approved