%I A004977
%S A004977 1,2,3,5,8,10,13,16,23,32,44,56,76,102,132,174,227,296,383,505,679,892,
%T A004977 1151,1516,1988,2602,3400,4410,5759,7519,9809,12810,16710,21758,28356,
%U A004977 36955,48189,62805,81803,106647,139088,181301,236453,308150,401689
%N A004977 Sum of digits of n-th term in Look and Say sequence A005150.
%C A004977 It appears that the ratio of consecutive terms approaches Conway's constant 
               1.303.. (A014715). The terms divided by the numbers of added digits 
               also would tend to a constant, i.e. A004977(n)/A005341(n)->const. 
               If the digits in A005150 occur with constant probabilities c1, c2, 
               c3 then A004977(n)=A005341(n)*(c1+2*c2+3*c3) and this conjecture 
               entails the convergences noted here. - Alexandre Losev (alosev(AT)svr.igic.bas.bg), 
               Aug 31 2005
%H A004977 Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003.html">
               International Contest Of Logical Sequences</a>, 2002 - 2003. Item 
               9
%H A004977 Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003ans.html">
               Solutions of International Contest Of Logical Sequences</a>, 2002 
               - 2003.
%t A004977 RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ 
               Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse 
               /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ 
               n, 1 ][ [ n ] ]; Table[ Apply[ Plus, F[ n ] ], {n, 1, 51} ]
%Y A004977 Cf. A005150.
%Y A004977 Cf. A005150, A005341, A014715.
%Y A004977 Sequence in context: A098177 A112045 A098389 this_sequence A094568 A022955 
               A087279
%Y A004977 Adjacent sequences: A004974 A004975 A004976 this_sequence A004978 A004979 
               A004980
%K A004977 nonn,base
%O A004977 1,2
%A A004977 Clark Kimberling (ck6(AT)evansville.edu)