A034002 A005150 expanded into single digits.

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

Offset

1,4

Comments

A005150(n) = Sum_{k=1..A005341(n)} T(n,k)*10^(A005341(n) - k). - Reinhard Zumkeller, Dec 15 2012

Links

Reinhard Zumkeller, Rows n = 1..25 of triangle, flattened

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. DOI: 10.1007/978-1-4612-4808-8_53.

M. Lothaire, Algebraic Combinatorics on Words, Cambridge, 2002, see p. 36.

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

Example

.  Initial rows                          A005150
.  1:  1                                           1
.  2:  1,1                                        11
.  3:  2,1                                        21
.  4:  1,2,1,1                                  1211
.  5:  1,1,1,2,2,1                            111221
.  6:  3,1,2,2,1,1                            312211
.  7:  1,3,1,1,2,2,2,1                      13112221
.  8:  1,1,1,3,2,1,3,2,1,1                1113213211
.  9:  3,1,1,3,1,2,1,1,1,3,1,2,2,1    31131211131221
-}

Prog

(Haskell)  see Watkins link, p. 3.
import Data.List (group)
a034002 n k = a034002_tabf !! (n-1) !! (k-1)
a034002_row n = a034002_tabf !! (n-1)
a034002_tabf = iterate
               (concat . map (\xs -> [length xs, head xs]) . group) [1]
-- Reinhard Zumkeller, Aug 09 2012
(Python)
from sympy import flatten
l=[1]
L=[1]
n=s=1
y=''
while n<21:
    x=str(l[n - 1]) + ' '
    for i in range(len(x) - 1):
        if x[i]==x[i + 1]: s+=1
        else:
            y+=str(s)+str(x[i])
            s=1
    x=''
    n+=1
    l.append(int(y))
    L.append([int(a) for a in list(y)])
    y=''
    s=1
print(l) # A005150
print(flatten(L)) # Indranil Ghosh, Jul 05 2017

Crossrefs

See the entry for A005150 for much more about this sequence.

Cf. A088203.

Cf. A005341 (row lengths), A220424 (method B version).

Sequence in context: A322351 A092523 A120891 * A276630 A176048 A359141

Adjacent sequences: A033999 A034000 A034001 * A034003 A034004 A034005

Keyword

nonn,base,tabf

Author

N. J. A. Sloane

Extensions

Offset changed and keyword tabf added by Reinhard Zumkeller, Aug 09 2012

Status

approved