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

1,2

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.

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 *)

Crossrefs

Cf. A005150.

Cf. A005150, A005341, A014715.

Sequence in context: A112045 A098389 A215260 * A186498 A226330 A226329

Adjacent sequences: A004974 A004975 A004976 * A004978 A004979 A004980

Keyword

nonn,base

Author

Clark Kimberling

Status

approved