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%I #44 Mar 02 2023 15:55:23
%S 0,10,1110,3110,132110,1113122110,311311222110,13211321322110,
%T 1113122113121113222110,31131122211311123113322110,
%U 132113213221133112132123222110,11131221131211132221232112111312111213322110,31131122211311123113321112131221123113111231121123222110
%N Describe the previous term! (method A - initial term is 0).
%C Method A = 'frequency' followed by 'digit'-indication.
%C a(n), A001140, A001141, A001143, A001145, A001151 and A001154 are all identical apart from the last digit of each term (the seed). This is because digits other than 1, 2 and 3 never arise elsewhere in the terms (other than at the end of each of them) of look-and-say sequences of this type (as is mentioned by Carmine Suriano in A006751). - _Chayim Lowen_, Jul 16 2015
%C a(n+1) - a(n) is divisible by 10^5 for n > 5. - _Altug Alkan_, Dec 04 2015
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
%D I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.
%H T. D. Noe, <a href="/A001155/b001155.txt">Table of n, a(n) for n=1..20</a>
%H J. H. Conway, <a href="http://dx.doi.org/10.1007/978-1-4612-4808-8_53">The weird and wonderful chemistry of audioactive decay</a>, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.
%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/cnwy/cnwy.html">Conway's Constant</a> [Broken link]
%H S. R. Finch, <a href="http://web.archive.org/web/20010207194413 /http://www.mathsoft.com/asolve/constant/cnwy/cnwy.html">Conway's Constant</a> [From the Wayback Machine]
%e The term after 3110 is obtained by saying "one 3, two 1's, one 0", which gives 132110.
%t A001155[1] := 0; A001155[n_] := A001155[n] = FromDigits[Flatten[{Length[#], First[#]}&/@Split[IntegerDigits[A001155[n-1]]]]]; Map[A001155,Range[15]] (* _Peter J. C. Moses_, Mar 21 2013 *)
%o (PARI) A001155(n,a=0)={ while(n--, 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]); a=concat(a)); a } \\ _M. F. Hasler_, Jun 30 2011
%o (Python)
%o from itertools import accumulate, groupby, repeat
%o def summarize(n, _): return int("".join(str(len(list(g)))+k for k, g in groupby(str(n))))
%o def aupton(terms): return list(accumulate(repeat(0, terms), summarize))
%o print(aupton(11)) # _Michael S. Branicky_, Jun 28 2022
%Y Cf. A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001151, A001154.
%Y Cf. A036058.
%K nonn,base,easy,nice
%O 1,2
%A _N. J. A. Sloane_
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