A001140 Describe the previous term! (method A - initial term is 4).

4, 14, 1114, 3114, 132114, 1113122114, 311311222114, 13211321322114, 1113122113121113222114, 31131122211311123113322114, 132113213221133112132123222114, 11131221131211132221232112111312111213322114, 31131122211311123113321112131221123113111231121123222114

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 3114 is obtained by saying "one 3, two 1's, one 4", which gives 132114.
		

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, A001141, A001143, A001145, A001151, A001154.

Programs

Haskell

cf. Josh Triplett's program for A005051.
import Data.List (group)
a001140 n = a001140_list !! (n-1)
a001140_list = 4 : map say a001140_list where
   say = read . concatMap saygroup . group . show
         where saygroup s = (show $ length s) ++ [head s]
-- 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, 4 ][ [ n ] ];
Table[ FromDigits[ F[ n ] ], {n, 1, 11} ] (* Zerinvary Lajos, Mar 21 2007 *)

Perl

# This outputs the first n elements of the sequence, where n is given on the command line.
$s = 4;
for (2..shift @ARGV) {
    print "$s, ";
    $s =~ s/(.)\1*/(length $&).$1/eg;
}
print "$s\n";
## Arne 'Timwi' Heizmann (timwi(AT)gmx.net), Mar 12 2008