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A005341 Length of n-th term in Look and Say sequences A005150 and A007651.
(Formerly M0321)
10
1, 2, 2, 4, 6, 6, 8, 10, 14, 20, 26, 34, 46, 62, 78, 102, 134, 176, 226, 302, 408, 528, 678, 904, 1182, 1540, 2012, 2606, 3410, 4462, 5808, 7586, 9898, 12884, 16774, 21890, 28528, 37158, 48410, 63138, 82350, 107312, 139984, 182376, 237746, 310036, 403966, 526646, 686646 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Row lengths of A034002 and of A220424. - Reinhard Zumkeller, Dec 15 2012
Satisfies a recurrence of order 72. The characteristic polynomial of this recurrence is a degree-72 polynomial that factors as (x-1)*q(x), where q(x) is a degree-71 polynomial. The unique positive real root of q is approximately 1.3036 and is called Conway's constant (A014715), which equals the limiting ratio a(n+1)/a(n). - Nathaniel Johnston, Apr 12 2018 [Corrected by Richard Stanley, Dec 26 2018]
REFERENCES
J. H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Communications, Springer, NY 1987, pp. 173-188.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..3000 (first 71 terms from Zak Seidov)
S. R. Finch, Conway's Constant.
S. R. Finch, Conway's Constant. [From the Wayback Machine]
Eric Weisstein's World of Mathematics, Look and Say Sequence.
FORMULA
a(n) = A055642(A005150(n)) = A055642(A007651(n)). - Reinhard Zumkeller, Dec 15 2012
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[ Length[ F[ n ] ], {n, 1, 51} ]
p = {12, -18, 18, -18, 18, -20, -22, 31, 15, -4, -4, -19, 62, -50, -21, -11, 41, 54, -56, -44, 15, -27, -15, 45, -8, 89, -64, -66, -25, 38, 126, -39, -32, -33, -65, 107, 14, 16, -13, -79, 7, 42, 12, 8, -26, -9, 35, -23, -20, -30, 34, 58, -1, -20, -36, -6, 13, 8, 6, 3, -1, -4, -1, -4, -5, -1, 8, 6, 0, -6, -4, 1, 0, 1, 1, 1, 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, 99}], x] (* Peter J. C. Moses, Jun 23 2013 *)
PROG
(PARI) print1(a=1); for(i=2, 100, print1(", ", #Str(a=A005150(2, a)))) \\ M. F. Hasler, Nov 08 2011
(Haskell)
a005341 = length . a034002_row -- Reinhard Zumkeller, Dec 15 2012
CROSSREFS
Sequence in context: A109832 A309075 A039731 * A137268 A008130 A055388
KEYWORD
nonn,base,easy,nice,changed
AUTHOR
EXTENSIONS
More terms from Mike Keith
STATUS
approved

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Last modified July 15 17:56 EDT 2024. Contains 374333 sequences. (Running on oeis4.)