A001151 Describe the previous term! (method A - initial term is 8).

8, 18, 1118, 3118, 132118, 1113122118, 311311222118, 13211321322118, 1113122113121113222118, 31131122211311123113322118, 132113213221133112132123222118

Offset

1,1

Comments

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

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

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]

Example

E.g. the term after 3118 is obtained by saying "one 3, two 1's, one 8", which gives 132118.

Maple

freq := proc(i, L)
    local f, p ;
    if i > nops(L) or i < 1 then
        return 0 ;
    end if;
    f := 1 ;
    for p from i to 2 by -1 do
        if op(p, L) = op(p-1, L) then
            f := f+1 ;
        else
            return f;
        end if;
    end do:
    f ;
end proc:
read("transforms"):
rle := proc(n)
    local inL, i, outL, f ;
    inL := convert(n, base, 10) ;
    i := nops(inL) ;
    outL := [] ;
    while i>0 do
        f := freq(i, inL) ;
        if f = 0 then
            break;
        else
            outL := [op(outL), f, op(i, inL)] ;
            i := i-f ;
        end if;
    end do:
    digcatL(outL) ;
end proc:
A001151 := proc(n)
    option remember ;
    if n = 1 then
        8;
    else
        rle(procname(n-1)) ;
    end if;
end proc:
seq(A001151(n), n=1..10) ; # R. J. Mathar, Feb 11 2021

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, 8][[n]]; Table[FromDigits[F[n]], {n, 1, 11}] (* Zerinvary Lajos, Jul 08 2009 *)

Crossrefs

Cf. A001155, A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001154.

Sequence in context: A171371 A092692 A338474 * A177367 A138492 A022512

Adjacent sequences: A001148 A001149 A001150 * A001152 A001153 A001154

Keyword

nonn,base,easy,nice

Author

N. J. A. Sloane

Status

approved