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%I #20 Jun 18 2013 12:25:55
%S 1,2,4,4,6,10,12,14,22,26,30,44,56,70,98,130,162,216,292,358,470,628,
%T 792,1050,1384,1788,2334,3072,3974,5162,6784,8786,11420,14992,19484,
%U 25388,33160,43262,56252,73392,95798,124496,162556,212048,275976,360154
%N Length of n-th term of A022470.
%C a(n) is the length of the n-th term of many sequences generated by methods A and B, including those shown here:
%C Method A, 1st term ... Method B, 1st term
%C A001155, 0
%C A006751, 2 ......... A022470, 2
%C A006715, 3 ......... A022499, 3
%C A001140, 4 ......... A022500, 4
%C A001141, 5 ......... A022501, 5
%C A001143, 6 ......... A022502, 6
%C A001145, 7 ......... A022503, 7
%C A001151, 8 ......... A022504, 8
%C A001154, 9 ......... A022505, 9
%C _Clark Kimberling_, Jun 14 2013
%H Peter J. C. Moses, <a href="/A022471/b022471.txt">Table of n, a(n) for n = 1..3000</a>
%t a[0] = 2; a[n_] := a[n] = FromDigits[Flatten[{First[#], Length[#]} & /@ Split[IntegerDigits[a[n - 1]]]]]; Map[Length[IntegerDigits[a[#]]] &, Range[0, 40]] (* _Peter J. C. Moses_, Jun 14 2013 *)
%t p = {9, -9, 6, -16, 5, 2, 0, -9, -1, -1, 20, 2, 6, -3, -15, -13, 15, 20, 15, -26, -28, 7, 6, 26, -27, -4, 9, -15, 3, 2, 8, 43, 9, -39, -24, -2, -24, 28, 9, 13, 13, -18, -12, -16, 14, 13, 16, 8, -36, 1, -6, -8, 15, 1, 14, 3, -6, -7, -3, 2, -2, 2, 2, 0, -1, -2, -1, 3, 3, -1, -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, 100}], x] (* _Peter J. C. Moses_, Jun 16 2013 *)
%Y Cf. A022470.
%K nonn
%O 1,2
%A _Clark Kimberling_
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