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A004977 Sum of digits of n-th term in Look and Say sequence A005150. 6

%I #16 Aug 11 2014 22:45:12

%S 1,2,3,5,8,10,13,16,23,32,44,56,76,102,132,174,227,296,383,505,679,

%T 892,1151,1516,1988,2602,3400,4410,5759,7519,9809,12810,16710,21758,

%U 28356,36955,48189,62805,81803,106647,139088,181301,236453,308150,401689

%N Sum of digits of n-th term in Look and Say sequence A005150.

%C 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_, Aug 31 2005

%H Peter J. C. Moses, <a href="/A004977/b004977.txt">Table of n, a(n) for n = 1..1000</a>

%H Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003.html">International Contest Of Logical Sequences</a>, 2002 - 2003. Item 9

%H Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003ans.html">Solutions of International Contest Of Logical Sequences</a>, 2002 - 2003.

%t 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} ]

%t p={-4,8,-7,-10,15,18,11,-65,-4,27,7,9,-62,47,56,-32,-46,-8,67,44,-16,24,2,-59,-20,-65,84,122,-51,-38,-131,10,91,24,39,-89,-42,39,12,45,-40,-63,39,40,10,-19,-58,47,51,-7,-43,-67,32,41,20,-13,-24,-3,8,0,0,0,0,10,5,-3,-11,-6,5,7,3,-2,-1,-1,-1,-1,0,1,1}; q={6,-9,9,-18,16,-11,14,-8,1,-5,7,2,8,-14,-5,-5,19,3,-6,-7,-6,16,-7,8,-22,17,-12,7,5,7,-8,4,-7,-9,13,-4,-6,14,-14,19,-7,-13,2,-4,18,0,-1,-4,-12,8,-5,0,8,1,7,-8,-5,-2,3,3,0,0,0,0,-2,-1,0,3,1,-1,-1,-1,1}; gf=Fold[x #1+#2&,0,p]/Fold[x #1+#2&,0,q]; CoefficientList[Series[gf,{x,0,99}],x] (* _Peter J. C. Moses_, Jun 24 2013 *)

%Y Cf. A005150.

%Y Cf. A005150, A005341, A014715.

%K nonn,base

%O 1,2

%A _Clark Kimberling_

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Last modified March 19 03:27 EDT 2024. Contains 370952 sequences. (Running on oeis4.)