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
KEYWORD
nonn,base,easy,nice
AUTHOR
STATUS
approved