A043276 -id:A043276 - cp's OEIS frontend

A043286 Maximal run length in base-12 representation of n.

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

Offset: 1

Clark Kimberling

For all numbers n in A023806, a(n)=1, but this holds also for others, e.g., n=145, not in A023806. The same relation holds for the terms of A113763 less than n=144, but becomes wrong from then on. - M. F. Hasler, Jul 24 2013

Antti Karttunen, Table of n, a(n) for n = 1..22621

Cf. A043276-A043290 for base-2 to base-16 analogs.

A043286[n_]:=Max[Map[Length,Split[IntegerDigits[n,12]]]];Array[A043286,100] (* Paolo Xausa, Sep 27 2023 *)

A043286(n, b=12){=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 - typos fixed by Antti Karttunen, Dec 06 2017

More terms from Antti Karttunen, Dec 06 2017

A175599 The difference between maximal run length and minimal run length in binary representation of n.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 2, 1, 0, 1, 0, 1, 2, 0, 3, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 2, 3, 0, 4, 3, 2, 2, 1, 1, 1, 2, 2, 1, 0, 1, 1, 1, 2, 3, 2, 2, 1, 0, 1, 1, 1, 2, 0, 2, 2, 2, 2, 3, 4, 0, 5, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 3, 4, 3, 3, 2, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Juri-Stepan Gerasimov, Jul 23 2010

a(n)=A043276(n)-A175597(n).

Terms checked by D. S. McNeil, Nov 26 2010

A227761 a(n) is the maximal difference between successive parts in the minimally runlength-encoded unordered partition of n (A227368(n)).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jul 26 2013

nonn

After n=3, only composites may obtain value 0. (But not all of them do; see A227762.) The first nine n for which a(n)=2 are 7, 13, 23, 33, 47, 61, 79, 97, 119, of which all are primes except 33 and 119. Conjecture: these values are given by A227786.

Are there any terms larger than 2?

Antti Karttunen, Table of n, a(n) for n = 0..132

A227762 gives the positions of zeros, in other words, such n that their minimally runlength-encoded partition consists of identical parts.

Cf. also A227368 (for the concept of minimally runlength-encoded unordered partition).

(define (A227761 n) (if (< n 2) 0 (- (A043276 (A163575 (A227368 n))) 1)))
;; Alternative version which uses auxiliary functions DIFF and binexp_to_ascpart which can be found in the Program section of A129594:
(define (A227761v2 n) (if (< n 2) 0 (apply max (DIFF (binexp_to_ascpart (A227368 n))))))

a(0) = a(1) = 0, and for n>1, a(n) = A043276(A163575(A227368(n))) - 1.

A037969 Numbers whose maximal base-2 run length is 2.

Original entry on oeis.org

3, 4, 6, 9, 11, 12, 13, 18, 19, 20, 22, 25, 26, 27, 36, 37, 38, 41, 43, 44, 45, 50, 51, 52, 53, 54, 73, 74, 75, 76, 77, 82, 83, 84, 86, 89, 90, 91, 100, 101, 102, 105, 106, 107, 108, 109, 146, 147, 148, 149, 150, 153, 154, 155, 164, 165

Offset: 1

Clark Kimberling

Cf. A000975 = { n | A043276(n)=1 }, A037970 ff.

Select[Range[200],Max[Length/@Split[IntegerDigits[#,2]]]==2&] (* Harvey P. Dale, Dec 20 2024 *)

for(i=1,199,A043276(i)==2&&print1(i",")) \\ M. F. Hasler, Jul 23 2013

A037969 = { n | A043276(n)=2 }. - M. F. Hasler, Jul 23 2013

A037971 Numbers whose maximal base-2 run length is 4.

Original entry on oeis.org

15, 16, 30, 33, 47, 48, 60, 61, 66, 67, 79, 80, 94, 97, 111, 112, 120, 121, 122, 123, 132, 133, 134, 135, 143, 144, 158, 161, 175, 176, 188, 189, 194, 195, 207, 208, 222, 225, 239, 240, 241, 242, 243, 244, 245, 246, 247, 264, 265

Offset: 1

Clark Kimberling

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A043276.

Select[Range[300],Max[Length/@Split[IntegerDigits[#,2]]]==4&] (* Harvey P. Dale, Apr 24 2019 *)

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

A175911 Concatenate the run lengths of the runs of ones and zeros in the binary representation of n in the lowest possible base where it is possible to represent each run length as a single digit. Convert the result to base 10.

Original entry on oeis.org

1, 3, 2, 5, 7, 7, 3, 7, 16, 15, 14, 8, 22, 13, 4, 9, 29, 49, 17, 41, 31, 43, 23, 11, 25, 67, 23, 14, 53, 21, 5, 11, 46, 117, 30, 50, 148, 52, 27, 87, 124, 63, 122, 44, 130, 93, 34, 14, 45, 76, 26, 68, 202, 70, 39, 15, 57, 213, 54, 22, 106, 31, 6, 13, 67, 231, 47, 118, 469, 121

Offset: 1

Dylan Hamilton, Oct 14 2010

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A043276.

Cf. A101211, A233836.

a175911 n = foldl1 (\v d -> b * v + d) rls where
   b = maximum rls + 1
   rls = a101211_row n
-- Reinhard Zumkeller, Dec 16 2013

repcount[x_] := Length/@Split[x]
binrep[x_] := repcount[IntegerDigits[x, 2]]
Table[h = binrep[x]; FromDigits[h, Max[h] + 1], {x, 1, DESIRED_NUMBER_OF_DIGITS}]
f[n_] := Block[{a = Length /@ Split@ IntegerDigits[n, 2]}, FromDigits[a, Max@ a + 1]]; Array[f, 70] (* Robert G. Wilson v, Aug 17 2013 *)

A175611 Primes p such that A175599(p)=0.

Original entry on oeis.org

2, 3, 5, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

Offset: 1

Juri-Stepan Gerasimov, Jul 24 2010

Primes p such that A043276(p)=A175597(p).

Charles R Greathouse IV, Table of n, a(n) for n = 1..20

Cf. A000668, A002450.

a(11)-a(14) from Charles R Greathouse IV, Jul 22 2016

A166110 A positive integer n is included if the longest contiguous run of similar digits in binary n is of 0's.

Original entry on oeis.org

2, 4, 5, 8, 9, 10, 12, 16, 17, 18, 19, 20, 21, 24, 25, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 51, 52, 56, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 88, 89, 96, 97, 98, 99, 100, 101, 102, 104, 105, 108, 112, 113, 128, 129

Offset: 1

Leroy Quet, Oct 06 2009

For some n included in this sequence, it is possible that the longest run of 0's in binary n is of the same length as the longest run of 1's in binary n. (See sequence A090050.)

Cf. A043276, A090050, A166111.

Extended by Ray Chandler, Mar 12 2010

cp's OEIS Frontend

A043286 Maximal run length in base-12 representation of n.

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A175599 The difference between maximal run length and minimal run length in binary representation of n.

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A227761 a(n) is the maximal difference between successive parts in the minimally runlength-encoded unordered partition of n (A227368(n)).

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A037969 Numbers whose maximal base-2 run length is 2.

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A037971 Numbers whose maximal base-2 run length is 4.

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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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A175911 Concatenate the run lengths of the runs of ones and zeros in the binary representation of n in the lowest possible base where it is possible to represent each run length as a single digit. Convert the result to base 10.

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A175611 Primes p such that A175599(p)=0.

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