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A004977
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Sum of digits of n-th term in Look and Say sequence A005150.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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