A044940 -id:A044940 - cp's OEIS frontend

A043283 Maximal run length in base-9 representation of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2

Offset: 1

Clark Kimberling

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

Cf. A007095.
Cf. A043276-A043290 for base-2 to base-16 analogs.
Cf. A002452 (gives the positions of records, the first occurrence of each n).
Cf. also A044940.

A043283[n_]:=Max[Map[Length,Split[IntegerDigits[n,9]]]];Array[A043283,100] (* Paolo Xausa, Sep 27 2023 *)

A043283(n, b=9)={my(m, c=1); while(n>0, n%b==(n\=b)%b && c++ && next; m=max(m, c); c=1); m} \\ M. F. Hasler, Jul 23 2013

A044931 a(n) = so-se, where so(se)=sum of odd(even) base 9 run lengths of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -1, 3, 3, 3, 3, 3, 3, 3, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, 3, 3

Offset: 1

Clark Kimberling

			From _Antti Karttunen_, Dec 16 2017: (Start)
For n = 82 = 1*(9^2) + 0*(9^1) + 1*(9^0), thus written as "101" in base 9, there are three odd runs (each of length 1) and no even runs, so a(82) = 3*1 = 3.
For n = 7383, "11113" in base 9, there is an even run of length 4 and an odd run of length 1, thus a(7383) = 1-4 = -3.
(End)

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

Cf. A043283, A044940.

Array[Total[Length /@ #1] - Total[Length /@ Complement[#2, #1]] & @@ {Select[#, OddQ@ Length@ # &], #} &@ Split@ IntegerDigits[#, 9] &, 100] (* Michael De Vlieger, Dec 16 2017 *)

A044931(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 += ((-1)^rl)*rl; prev_d = d; rl = 1)); -(s + ((-1)^rl)*rl); }; \\ Antti Karttunen, Dec 16 2017

More terms from Antti Karttunen, Dec 16 2017

A043536 Number of distinct base-9 digits of n.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

			As 731 = 1*(9^3) + 0*(9^2) + 0*(9^1) + 2*(9^0), it is written in base 9 (A007095) as "1002". There are three kinds of digits present, thus a(731) = 3. - _Antti Karttunen_, Dec 22 2017

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

Cf. A007095, A043283, A044931, A044940, A044949.

Table[Count[DigitCount[n,9],+?(#>0&)],{n,100}] (* _Harvey P. Dale, Apr 30 2015 *)

A043536(n) = length(vecsort(digits(n,9),,8)); \\ Antti Karttunen, Dec 22 2017

More terms from Antti Karttunen, Dec 22 2017

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

Original entry on oeis.org

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

Clark Kimberling

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

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

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

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

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

More terms from Antti Karttunen, Dec 22 2017

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A043283 Maximal run length in base-9 representation of n.

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A044931 a(n) = so-se, where so(se)=sum of odd(even) base 9 run lengths of n.

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A043536 Number of distinct base-9 digits of n.

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

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