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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
Albert Frank, International Contest Of Logical Sequences, 2002 - 2003. Item 9
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.
Sequence in context: A112045 A098389 A215260 * A186498 A226330 A226329
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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