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 A006751 Describe the previous term! (method A - initial term is 2). (Formerly M2052) 29
 2, 12, 1112, 3112, 132112, 1113122112, 311311222112, 13211321322112, 1113122113121113222112, 31131122211311123113322112, 132113213221133112132123222112, 11131221131211132221232112111312111213322112, 31131122211311123113321112131221123113111231121123222112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Method A = 'frequency' followed by 'digit'-indication. No digit exceeds 3. If the starting number a(1) is a single-digit number greater than 3 this will remain as the last digit, all the remaining in any term being no greater than 3. - Carmine Suriano, Sep 07 2010 a(n) = value of concatenation of n-th row in A088203. - Reinhard Zumkeller, Aug 09 2012 This is because for all n > 1, a(n) begins with 1 or 3 and ends with 2. - Jean-Christophe Hervé, May 07 2013 a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4. LINKS T. D. Noe, Table of n, a(n) for n=1..20 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. S. R. Finch, Conway's Constant [Broken link] S. R. Finch, Conway's Constant [From the Wayback Machine] Eric Weisstein's World of Mathematics, Look and Say Sequence FORMULA a(n+1) = A045918(a(n)). - Reinhard Zumkeller, Aug 09 2012 EXAMPLE E.g. the term after 3112 is obtained by saying "one 3, two 1's, one 2", which gives 132112. MATHEMATICA RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ n, 2 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 11} ] (* Zerinvary Lajos, Mar 21 2007 *) PROG (Haskell) a006751 = foldl1 (\v d -> 10 * v + d) . map toInteger . a088203_row -- Reinhard Zumkeller, Aug 09 2012 (Perl) # This outputs the first n elements of the sequence, where n is given on the command line. \$s = 2; for (2..shift @ARGV) { print "\$s, "; \$s =~ s/(.)\1*/(length \$&).\$1/eg; } print "\$s\n"; ## Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008) (Python) l=[2] 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)) y='' s=1 print(l) # Indranil Ghosh, Jul 05 2017 CROSSREFS Cf. A001140, A001141, A001143, A001145, A001151, A001154, A001155, A005150, A006715, A045918. Cf. A088203 (continuous version). Sequence in context: A057120 A345976 A112512 * A023989 A001389 A022914 Adjacent sequences: A006748 A006749 A006750 * A006752 A006753 A006754 KEYWORD nonn,base,easy,nice AUTHOR N. J. A. Sloane STATUS approved

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Last modified April 13 18:35 EDT 2024. Contains 371644 sequences. (Running on oeis4.)