cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A143586 Length of row n of the Kolakoski fan A143477.

Original entry on oeis.org

1, 1, 2, 4, 6, 9, 13, 19, 29, 44, 66, 99, 151, 225, 338, 506, 761, 1138, 1705, 2555, 3835, 5751, 8629, 12953, 19426, 29146, 43723, 65585, 98351, 147501, 221259, 331899, 497861, 746874, 1120279, 1680480, 2520838, 3781134, 5671673, 8507660, 12761336
Offset: 1

Views

Author

Clark Kimberling, Aug 25 2008

Keywords

Comments

Conjecture: if L(n)=A143586(n), then lim(L(n+1)/L(n)) = 3/2. For a more general conjecture see A143589.

Examples

			The first 4 rows of A143477 are
1
2
22
1122. Their lengths are 1,1,2,4.

Crossrefs

Cf. A000002, A143477.

A143587 Number of 1's in row n of the Kolakoski fan A143477.

Original entry on oeis.org

1, 0, 0, 2, 3, 5, 7, 9, 14, 22, 33, 47, 77, 112, 170, 251, 384, 571, 855, 1275, 1919, 2873, 4305, 6480, 9706, 14569, 21861, 32819, 49201, 73743, 110619, 165937, 248848, 373469, 560078, 840122, 1260542, 1890595, 2835686, 4253984, 6380906, 9571020
Offset: 1

Views

Author

Clark Kimberling, Aug 25 2008

Keywords

Comments

A143586 = A143587 + A143588.

Examples

			The first 4 rows of A143477 are 1; 2; 22; 1122. The respective numbers of 1's are 1,0,0,2.

Crossrefs

Cf. A000002, A143477, A143486, A143588.

A143588 Number of 2's in row n of the Kolakoski fan A143477.

Original entry on oeis.org

0, 1, 2, 2, 3, 4, 6, 10, 15, 22, 33, 52, 74, 113, 168, 255, 377, 567, 850, 1280, 1916, 2878, 4324, 6473, 9720, 14577, 21862, 32766, 49150, 73758, 110640, 165962, 249013, 373405, 560201, 840358, 1260296, 1890539, 2835987, 4253676, 6380430, 9570746
Offset: 1

Views

Author

Clark Kimberling, Aug 25 2008

Keywords

Comments

A143586 = A143587 + A143588.

Examples

			The first 4 rows of A143477 are 1; 2; 22; 1122. The respective numbers of 1's are 0,1,2,2.

Crossrefs

Cf. A000002, A143477, A143486, A143487.

A143589 Kolakoski fan based on A000034 with initial row 1.

Original entry on oeis.org

1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1
Offset: 1

Views

Author

Clark Kimberling, Aug 25 2008

Keywords

Comments

Conjecture (following Benoit Cloitre's conjecture at A111090): if L(n) is the number (assumed finite) of terms in row n of K, then L(n)*(2/3)^n approaches a constant. (L= A143590.)

Examples

			s=(1,2,1,2,1,2,1,2,...) and w=1, so the first 7 rows are
1
2
1 1
2 1
1 1 2
2 1 2 2
1 1 2 1 1 2 2

Crossrefs

Cf. A000002, A143477, A143490.

Formula

Introduced here is an array K called the "Kolakoski fan based on a sequence s with initial row w": suppose that s=(s(1),s(2),...) is a sequence of 1's and 2's and that w=(w(1),w(2),...) is a finite or infinite sequence of 1's and 2's. Assume that s(1)=w(1) and that if w(1)=1 then s contains at least one 2. Row 1 of the array K is w. Subsequent rows are defined inductively: the first term of row n is s(n) and the remaining terms are defined by Kolakoski substitution; viz., each number in row n-1 tells the string-length (1 or 2) of the next string in row n, each term being either 1 or 2.

A143590 Length of row n of A143589 (a Kolakoski fan).

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 7, 10, 16, 24, 36, 54, 80, 120, 180, 269, 404, 605, 908, 1361, 2041, 3063, 4591, 6890, 10333, 15509, 23259, 34901, 52344, 78516, 117762, 176636, 264944, 397405, 596099, 894193, 1341290, 2011935, 3017927, 4526825
Offset: 1

Views

Author

Clark Kimberling, Aug 25 2008

Keywords

Comments

Conjecture (following Benoit Cloitre's conjecture at A111090):
if L=A143489, then L(n)*(2/3)^n approaches a constant.

Examples

			The first 6 rows of A143589 are 1; 2; 1,1; 2,1; 1,1,2; 2,1,2,2. Their
lengths are 1,1,2,2,3,4.

Crossrefs

Cf. A000002, A111090, A143477, A143586, A143489.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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