A043283 -id:A043283 - cp's OEIS frontend

A043290 Maximal run length in base 16 representation of n.

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

Offset: 1

Clark Kimberling

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A043276, A043277, A043278, A043279, A043280, A043281, A043282, A043283, A043284, A043285, A043286, A043287, A043288, A043289 for base-2 to base-15 analogs.

A043290[n_]:=Max[Map[Length,Split[IntegerDigits[n,16]]]];Array[A043290,100] (* Paolo Xausa, Sep 27 2023 *)

A043290(n,b=16)={my(m,c=1);while(n>0,n%b==(n\=b)%b && c++ && next;m=max(m,c);c=1);m} \\ Use optional 2nd arg to get sequences A043276 through A043289. - M. F. Hasler, Jul 23 2013

from itertools import groupby
def A043290(n): return max(len(list(g)) for k, g in groupby(hex(n)[2:])) # Chai Wah Wu, Mar 09 2023

More terms from Antti Karttunen, Sep 21 2018

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

Original entry on oeis.org

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

Clark Kimberling

			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)

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

Cf. A043283, A044931.

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

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

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

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

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

A043287 Maximal run length in base-13 representation of n.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A043276, A043277, A043278, A043279, A043280, A043281, A043282, A043283, A043284, A043285, A043286, A043288, A043289, A043290 for base-2 to base-16 analogs.

A043287[n_]:=Max[Map[Length,Split[IntegerDigits[n,13]]]];Array[A043287,100] (* Paolo Xausa, Sep 27 2023 *)

A043287(n,b=13)={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

More terms from Antti Karttunen, Sep 21 2018

A043288 Maximal run length in base-14 representation of n.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A043276, A043277, A043278, A043279, A043280, A043281, A043282, A043283, A043284, A043285, A043286, A043287, A043289, A043290 for base-2 to base-16 analogs.

A043288[n_]:=Max[Map[Length,Split[IntegerDigits[n,14]]]];Array[A043288,100] (* Paolo Xausa, Sep 27 2023 *)

A043288(n,b=14)={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

More terms from Antti Karttunen, Sep 21 2018

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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A043290 Maximal run length in base 16 representation of n.

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A044940 Number of runs of even 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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A043287 Maximal run length in base-13 representation of n.

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A043288 Maximal run length in base-14 representation 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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