A022303 -id:A022303 - cp's OEIS frontend

A022305 Exactly half the first a(n) terms of A022303 are 1's.

2, 4, 6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 32, 34, 36, 38, 40, 42, 44, 46, 50, 52, 54, 56, 58, 60, 64, 66, 68, 70, 72, 74, 76, 78, 82, 84, 94, 100, 102, 112, 114, 118, 120, 122, 124, 126, 128, 132, 134, 136, 138, 140, 142, 144, 146, 148, 154, 156, 158

Offset: 0

Clark Kimberling

nonn

A022304 Index of n-th 1 in A022303.

Original entry on oeis.org

1, 3, 6, 9, 10, 12, 13, 16, 18, 19, 21, 24, 25, 27, 28, 30, 33, 36, 37, 39, 42, 44, 45, 47, 48, 51, 54, 55, 57, 60, 63, 64, 66, 67, 69, 72, 74, 75, 78, 81, 82, 84, 87, 90, 91, 93, 94, 97, 99, 100, 102, 105, 108, 109, 111, 112, 114, 117, 118, 120, 121, 124

Offset: 0

Clark Kimberling

nonn

A025516 Index of n-th 2 in A022303.

Original entry on oeis.org

2, 4, 5, 7, 8, 11, 14, 15, 17, 20, 22, 23, 26, 29, 31, 32, 34, 35, 38, 40, 41, 43, 46, 49, 50, 52, 53, 56, 58, 59, 61, 62, 65, 68, 70, 71, 73, 76, 77, 79, 80, 83, 85, 86, 88, 89, 92, 95, 96, 98, 101, 103, 104, 106, 107, 110, 113, 115, 116, 119, 122, 123, 125, 128, 131, 132, 134

Offset: 1

David W. Wilson

nonn

A025517 Least k such that first k terms of A022303 contain n more 1's than 2's.

Original entry on oeis.org

1, 28, 253, 794, 821, 854, 1123, 1394, 1493, 1520, 1529, 193136, 193169, 194032, 194041, 195374, 196367, 196376, 198567, 198630, 199145, 199550, 199857, 200282, 201755, 201782, 201791, 205326, 205683, 205710, 205803, 206028, 206061, 206088

Offset: 1

David W. Wilson

nonn

A025518 Least k such that first k terms of A022303 contain n more 2's than 1's.

Original entry on oeis.org

5, 8, 89, 374, 467, 6348, 6965, 7172, 7265, 7562, 7967, 20334, 20367, 21978, 22005, 25634, 25661, 25688, 27965, 39180, 39207, 42394, 43125, 43146, 48633, 48726, 48753, 49010, 49037, 49064, 49091, 49860, 50077, 50086, 50383, 50410, 50955, 51340, 52239

Offset: 1

David W. Wilson

nonn

A025519 Least k>1 such that first n terms of A022303 repeat beginning at k-th term.

Original entry on oeis.org

3, 3, 10, 19, 19, 19, 28, 28, 28, 28, 28, 28, 55, 55, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 460, 460, 460, 460, 460, 460, 460, 460, 460, 460, 460, 460, 460, 460, 460, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 1096, 8079

Offset: 1

David W. Wilson

nonn

A025520 Least k>1 such that reverse of first n terms of A022303 repeats beginning at k-th term.

Original entry on oeis.org

3, 2, 10, 15, 14, 13, 38, 146, 145, 144, 143, 142, 222, 221, 220, 219, 218, 217, 216, 215, 214, 374, 373, 372, 574, 573, 572, 571, 570, 569, 568, 567, 566, 565, 564, 563, 562, 561, 560, 7694, 7693, 7692, 7691, 7690, 7689, 7688, 7687, 7686, 7685, 7684, 7683, 7682

Offset: 1

David W. Wilson

nonn

A025521 Least k>1 such that complement of first n terms of A022303 repeats beginning at k-th term.

Original entry on oeis.org

2, 2, 2, 15, 15, 15, 15, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 123, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691, 691

Offset: 1

David W. Wilson

nonn

A025522 Least k>1 such that reverse complement of first n terms of A022303 repeats beginning at k-th term.

Original entry on oeis.org

2, 3, 2, 19, 18, 17, 16, 24, 23, 22, 21, 20, 58, 57, 341, 340, 339, 338, 337, 336, 335, 334, 333, 332, 331, 330, 329, 328, 327, 326, 325, 324, 323, 322, 649, 648, 647, 646, 645, 863, 862, 861, 860, 859, 858, 857, 856, 855, 854, 853, 852, 851, 850, 849, 848, 847, 846, 845

Offset: 1

David W. Wilson

nonn

A022300 The sequence a of 1's and 2's starting with (1,1,2,1) such that a(n) is the length of the (n+2)nd run of a.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling

nonn

It appears that various properties and unsolved problems associated with the Kolakoski sequence, A000002, apply also to A022300.

			a(1) =1, so the 3rd run has length 1, so a(5) must be 2.
a(2) = 1, so the 4th run has length 1, so a(6) = 1.
a(3) = 2, so the 5th run has length 2, so a(7) = 1 and a(8) = 2.
a(4) = 1, so the 6th run has length 1, so a(9) = 1.
Globally, the runlength sequence of a is 2,1,1,1,2,1,2,1,1,2,1,1,2,...., and deleting the first two terms leaves a = A022300.

Clark Kimberling, Table of n, a(n) for n = 1..20000

Cf. A022303, A006928, A000002.

a = {1, 1, 2}; Do[a = Join[a, ConstantArray[If[Last[a] == 1, 2, 1], {a[[n]]}]], {n, 200}]; a
(* Peter J. C. Moses, Apr 01 2016 *)

Clarified and augmented by Clark Kimberling, Apr 02 2016

cp's OEIS Frontend

A022305 Exactly half the first a(n) terms of A022303 are 1's.

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A022304 Index of n-th 1 in A022303.

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A025516 Index of n-th 2 in A022303.

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A025517 Least k such that first k terms of A022303 contain n more 1's than 2's.

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A025518 Least k such that first k terms of A022303 contain n more 2's than 1's.

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A025519 Least k>1 such that first n terms of A022303 repeat beginning at k-th term.

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A025520 Least k>1 such that reverse of first n terms of A022303 repeats beginning at k-th term.

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A025521 Least k>1 such that complement of first n terms of A022303 repeats beginning at k-th term.

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A025522 Least k>1 such that reverse complement of first n terms of A022303 repeats beginning at k-th term.

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A022300 The sequence a of 1's and 2's starting with (1,1,2,1) such that a(n) is the length of the (n+2)nd run of a.

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