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 A004977 Sum of digits of n-th term in Look and Say sequence A005150. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 19 16:24 EDT 2024. Contains 374410 sequences. (Running on oeis4.)