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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• tabf

Examples

			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
		

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

Crossrefs

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

Cf. A088203.

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

Programs

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

Formula

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

Extensions

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