0,1

a(1111111111) = a((10^10 - 1)/9) = 101 is the first term with an odd number of digits; 3-digit terms are unambiguous, but already the 2nd 4-digit term is LS( 12 ) = 1112 = LS( 2*(10^111-1)/9 ) ( "hundred eleven 2's" ). The smallest n such that LS(n) = LS(k) for some k < n (i.e. the largest n such that the restriction of LS to [0..n-1] is injective) appears to be 10*(10^11 - 1)/9: LS(eleven '1's, one '0') = 11110 = LS(one '1', eleven '0's). -M. F. Hasler,Nov 14 2006

A121993gives numbers m such that a(m) < m. -Reinhard Zumkeller,Jan 25 2014

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,Table of n, a(n) for n = 0..10000

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

23 has "one 2, one 3", so a(23) = 1213.

LS:=n-> if n>9 then LS(op(convert(n, base, 10))) else for i from 2 to nargs do if args[i] <> n then RETURN(( LS( args[i..nargs] )*10^length(i-1) + i-1)*10 + n ) fi od: 10*nargs + n fi; #M. F. Hasler,Nov 14 2006

LookAndSayA[n_]:= FromDigits@ Flatten@ IntegerDigits@ Flatten[ Through[{Length, First}[#]] & /@ Split@ IntegerDigits@ n] (*Robert G. Wilson v,Jan 27 2012 *)

(PARI)A045918(a)={my(c=1); for(j=2, #a=Vec(Str(a)), if(a[j-1]==a[j], a[j-1]= ""; c++, a[j-1]=Str(c, a[j-1]); c=1)); a[#a]=Str(c, a[#a]); eval(concat(a))} \\M. F. Hasler,Jan 27 2012

(Haskell) see Watkins link, p. 3.

import Data.List (unfoldr, group); import Data.Tuple (swap)

a045918 0 = 10

a045918 n = foldl (\v d -> 10 * v + d) 0 $ say $ reverse $ unfoldr

(\x -> if x == 0 then Nothing else Just $ swap $ divMod x 10) n

where say = concat. map code. group

code xs = [toInteger $ length xs, head xs]

--Reinhard Zumkeller,Aug 09 2012

(Python)

from re import finditer

defA045918(n):

return int(''.join([str(len(m.group(0)))+m.group(0)[0] for m in finditer(r'(\d)\1*', str(n))]))

#Chai Wah Wu,Dec 03 2014

(Python)

from itertools import groupby

def LS(n): return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))

print([LS(n) for n in range(48)]) #Michael S. Branicky,Jul 27 2022

Cf.A005150.See alsoA056815.

Sequence in context:A047842A047843A097598*A244112A088476A248014

Adjacent sequences:A045915A045916A045917*A045919A045920A045921

nonn,base

Added Mma program fromA056815.-N. J. A. Sloane,Feb 02 2012

approved