The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Zak Seidov and 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] Christoph Koutschan,Regular Languages and their Generating Functions: The Inverse Problem 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 Adjacent sequences:  A005338 A005339 A005340 * A005342 A005343 A005344 KEYWORD nonn,base,easy,nice AUTHOR EXTENSIONS More terms from Mike Keith (Domnei(AT)aol.com) STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)