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

1,810

Links

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

Example

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)

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 *)

Prog

(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

Crossrefs

Cf. A043283, A044931.

Sequence in context: A369660 A353495 A302047 * A284261 A037825 A278701

Adjacent sequences: A044937 A044938 A044939 * A044941 A044942 A044943

Keyword

nonn,base

Author

Clark Kimberling

Extensions

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

Status

approved