A044949 Number of runs of odd length in the base-9 representation of n.

1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 3, 3, 3, 3

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..66430

Crossrefs

Cf. A007095, A043283, A043536, A044940, A044931.

Programs

Mathematica

Array[Count[Map[Length, Split@ IntegerDigits[#, 9]], ?OddQ] &, 105] (* _Michael De Vlieger, Dec 22 2017 *)

PARI

A044949(n) = { my(rl=0, d, prev_d = -1, s=0); while(n>0, d = (n%9); n = ((n-d)/9); if(d==prev_d, rl++, s += (rl%2); prev_d = d; rl = 1)); (s + (rl%2)); }; \\ Antti Karttunen, Dec 22 2017

Formula

As 731 = 1*(9^3) + 0*(9^2) + 0*(9^1) + 2*(9^0), it is written in base 9 (A007095) as "1002". There is one run of even length, and two runs of length 1 (thus of odd length), thus a(731) = 2. - Antti Karttunen, Dec 22 2017

Extensions

More terms from Antti Karttunen, Dec 22 2017