A087282 -id:A087282 - cp's OEIS frontend

A088203 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=2.

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

Offset: 1

Paul D. Hanna, Sep 22 2003

A006751(n) = concatenation of n-th row. - Reinhard Zumkeller, Aug 09 2012
From Jean-Christophe Hervé, May 07 2013: (Start)
The sequence is obtained continuously by applying the look-and-say rule from seed 2: 2 -> 1,2 -> 1,1,1,2 -> etc. The sequence is then determined by pairs of digits. Terms of even ranks are counts while odd ranks are figures. A225224 and A221646 are from seed 1 and A088204 from seed 3.
The present sequence is the concatenation of A006751 (original look-and-say method by blocks) because, with seed 2, all blocks of A006751 begin with 1 or 3 and end with 2 and therefore, there is no possible interaction between blocks after concatenation. (End)

J. H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.

Reinhard Zumkeller, Rows n = 1..25 of triangle, flattened
Kevin Watkins, Abstract Interpretation Using Laziness: Proving Conway's Lost Cosmological Theorem,
Kevin Watkins, Proving Conway's Lost Cosmological Theorem, POP seminar talk, CMU, Dec 2006
Eric Weisstein's World of Mathematics, Look and Say Sequence
Wikipedia, Look-and-say sequence

Cf. A088204, A087282, A005150.
Cf. A034002, A005150, A006751.
Cf. A225224, A221646 (seed one).

-- see Watkins link, p. 3.
import Data.List (group)
a088203 n k = a088203_tabf !! (n-1) !! (k-1)
a088203_row n = a088203_tabf !! (n-1)
a088203_tabf = iterate
               (concat . map (\xs -> [length xs, head xs]) . group) [2]
-- Reinhard Zumkeller, Aug 09 2012

A088204 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=3.

Original entry on oeis.org

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

Offset: 1

Paul D. Hanna, Sep 22 2003

The sequence is obtained continuously by applying the look-and-say rule from seed 3 : 3 -> 1,3 -> 1,1,1,3 -> etc. The sequence is then determined by pairs of digits. Terms of even ranks are counts while odd ranks are figures. A225224 and A221646 are from seed 1 and A088203 from seed 2. [Jean-Christophe Hervé, May 07 2013]

Cf. A088203, A087282, A005150, A006715.

Cf. A225224, A221646 (seed one).

A087283 An infinite audioactive word, one of three in the cycle that results from the limit of the 'Look and Say' sequence using method A with an initial term of 1 (A005150).

Original entry on oeis.org

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

Offset: 1

Paul D. Hanna, Aug 28 2003

Performing 'Look and Say' once generates A087284, twice results in A087282, while three operations yield the original infinite word.

Cf. A005150, A087284, A087282.

A087284 An infinite audioactive word, one of three in the cycle that results from the limit of the 'Look and Say' sequence using method A with an initial term of 1 (A005150).

Original entry on oeis.org

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

Offset: 1

Paul D. Hanna, Aug 28 2003

Performing 'Look and Say' once generates A087282, twice results in A087283, while three operations yield the original infinite word.

Cf. A005150, A087282, A087283.

A088205 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(0)=0.

Original entry on oeis.org

0, 1, 0, 1, 1, 1, 0, 3, 1, 1, 0, 1, 3, 2, 1, 1, 0, 1, 1, 1, 3, 1, 2, 2, 1, 1, 0, 3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 0, 1, 3, 2, 1, 1, 3, 2, 1, 3, 2, 2, 1, 1, 0, 1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 1, 3, 2, 2, 2, 1, 1, 0, 3, 1, 1, 3, 1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 1, 2, 3, 1, 1, 3, 3, 2, 2, 1, 1, 0, 1, 3, 2, 1

Offset: 0

Paul D. Hanna, Sep 22 2003

nonn

Positions of zero are given by A088206.

The sequence is obtained by starting with 0 and then successively appending the count (number of repetitions) and the value which is seen, term after term: "one zero, one one, one zero, three ones, one zero, ...". Otherwise said, the sequence is defined by "Start with 0 and append the result of "Look and Say" applied to the sequence". The "shifted left under Look and Say" property is thus an immediate consequence of the definition. A less trivial property is that there cannot be a number larger than 3 in this sequence. - M. F. Hasler, Jul 28 2015

			The initial terms {0,1,0,1,1,1,0,3,1,1,0,...} are shifted 1 place left by saying: "one 0, one 1, one 0, three 1's, one 0, ...", which drops the leading 0 to give {1,0,1,1,1,0,3,1,1,0,...}.

Cf. A088206, A088203, A087282, A005150.

a=List(0);my(i=1);while(#a<200,listput(a,1);listput(a,a[i]);while(a[i++]==a[#a],a[#a-1]++));a \\ M. F. Hasler, Jul 28 2015

A088206 Positions of zero in the infinite audioactive word, A088205, which shifts left under "Look and Say" method A, starting with a(1)=0.

Original entry on oeis.org

1, 3, 7, 11, 17, 27, 39, 53, 75, 101, 131, 175, 231, 301, 399, 529, 691, 907, 1199, 1557, 2027, 2655, 3447, 4497, 5881, 7669, 10003, 13075, 17049, 22211, 28995, 37781, 49201, 64193

Offset: 1

Paul D. Hanna, Sep 22 2003

Empirically the partial sums of A022471. - Sean A. Irvine, Jul 13 2022

			The initial terms of A088205, {0,1,0,1,1,1,0,3,1,1,0,...}, are shift left by saying: "one 0, one 1, one 0, three 1's, one 0, ...", which drops the leading 0 to give {1,0,1,1,1,0,3,1,1,0,...}.

Cf. A088205, A088203, A087282, A005150, A022471.

cp's OEIS Frontend

A088203 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=2.

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Haskell

A088204 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(1)=3.

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A087283 An infinite audioactive word, one of three in the cycle that results from the limit of the 'Look and Say' sequence using method A with an initial term of 1 (A005150).

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A087284 An infinite audioactive word, one of three in the cycle that results from the limit of the 'Look and Say' sequence using method A with an initial term of 1 (A005150).

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A088205 Infinite audioactive word that shifts 1 place left under "Look and Say" method A, starting with a(0)=0.

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PARI

A088206 Positions of zero in the infinite audioactive word, A088205, which shifts left under "Look and Say" method A, starting with a(1)=0.

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