A001141 Describe the previous term! (method A - initial term is 5).

5, 15, 1115, 3115, 132115, 1113122115, 311311222115, 13211321322115, 1113122113121113222115, 31131122211311123113322115, 132113213221133112132123222115

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

Method A = 'frequency' followed by 'digit'-indication.

A001155, A001140, A001141, A001143, A001145, A001151 and A001154 are all identical apart from the last digit of each term (the seed). This is because digits other than 1, 2 and 3 never arise elsewhere in the terms (other than at the end of each of them) of look-and-say sequences of this type (as is mentioned by Carmine Suriano in A006751). - Chayim Lowen, Jul 16 2015

a(n+1) - a(n) is divisible by 10^5 for n > 5. - Altug Alkan, Dec 04 2015

Examples

			The term after 3115 is obtained by saying "one 3, two 1's, one 5", which gives 132115.
		

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
• I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.

Links

• T. D. Noe, Table of n, a(n) for n=1..20
• J. H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.
• S. R. Finch, Conway's Constant [Broken link]
• S. R. Finch, Conway's Constant [From the Wayback Machine]

Crossrefs

Cf. A001155, A005150, A006751, A006715, A001140, A001143, A001145, A001151, A001154.

Programs

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, 5 ][ [ n ] ];
Table[ FromDigits[ F[ n ] ], {n, 1, 11} ] (* Zerinvary Lajos, Mar 21 2007 *)