A044940 Number of runs of even length in base-9 representation of n.

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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Examples

			From _Antti Karttunen_, Dec 15 2017: (Start)
For n = 810 = 729 + 81 = 9^3 + 9^2 thus in base 9 written as "1100", we count two runs, both of length 2, thus both even, so a(810) = 2.
For n = 32805 = 5*(9^4), thus in base 9 "50000", there is one run of even length, so a(32805) = 1.
For n = 65630 = 1*(9^5) + 1*(9^4) + 0*(9^3) + 0*(9^2) + 2*(9^1) + 2*(9^0) thus written as "110022" in base 9, there are three runs, all of length 2, thus all even, so a(65630) = 3.
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A043283, A044931.

Programs

Maple

f:= proc(n) local i,j,t,Q,d;
Q:= convert(n,base,9);
d:= nops(Q);
i:= 1: t:= 0:
while i < d do
   for j from i+1 to d while Q[j] = Q[i] do od:
   if (j-i)::even then t:= t+1 fi;
   i:= j;
od;
t
end proc:
map(f, [$1..100]); # Robert Israel, Dec 15 2017

Mathematica

a[n_] := Count[Length /@ Split[IntegerDigits[n, 9]], _?EvenQ];
Array[a, 120] (* Jean-François Alcover, Dec 16 2017 *)

PARI

A044940(n) = { my(rl=1, d, prev_d = -1, s=0); while(n>0, d = (n%9); n = ((n-d)/9); if(d==prev_d, rl++, s += (1-(rl%2)); prev_d = d; rl = 1)); (s + (1-(rl%2))); }; \\ Antti Karttunen, Dec 15 2017

Extensions

More terms and secondary offset added by Antti Karttunen, Dec 15 2017