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

1, 2, 3, 5, 8, 10, 13, 16, 23, 32, 44, 56, 76, 102, 132, 174, 227, 296, 383, 505, 679, 892, 1151, 1516, 1988, 2602, 3400, 4410, 5759, 7519, 9809, 12810, 16710, 21758, 28356, 36955, 48189, 62805, 81803, 106647, 139088, 181301, 236453, 308150, 401689

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

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

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000
• Albert Frank, International Contest Of Logical Sequences, 2002 - 2003. Item 9
• Albert Frank, Solutions of International Contest Of Logical Sequences, 2002 - 2003.

Crossrefs

Cf. A005150.

Cf. A005150, A005341, A014715.

Programs

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, 1 ][ [ n ] ]; Table[ Apply[ Plus, F[ n ] ], {n, 1, 51} ]
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 *)