This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
To get the term after 172113, we say: one 3's, three 1's, one 2's, one 7's, so 13311217
To get the term after 182113, we say: one 3's, three 1's, one 2's, one 8's, so 13311218
To get the term after 13213141, we say: four 1's, one 2, two 3's, one 4; therefore 14213241 (digit named before frequency).
RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split@ Sort@x; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ n, 1 ][ [ n ] ]; Table[ FromDigits[ F[ n ] ], {n, 1, 15} ] (* Robert G. Wilson v Sep 11 2006 *)
Start with 1. There is one 1: 11 and 1+1=2. The sequence is now 1,2. Therefore one 1 and one 2: 1112 and 1+1+1+2=5. The sequence is now 1,2,5. Again: 111215 and 1+1+1+2+1+5=11. And so on.
sd:=proc(j)
local c,d,h,k;
h:=j; c:=0;
if h>0 then
d:=floor(evalf(log10(h))+1);
for k from 1 to d do c:=c+h-10*trunc(h/10); h:=trunc(h/10); od;
fi;
c;
end:
P:=proc(i)
local a,b,f,n,p,s,v;
v:=array[10]; v[1]:=1; v[10]:=0; print(v[1]);
for n from 2 to 9 do v[n]:=0; od;
for n from 1 by 1 to i do
a:=0;
for p from 1 to 10 do
if sd(v[p])=0 then a:=a+sd(v[p]);
else a:=a+(p mod 10)+sd(v[p]);
fi;
od;
print(a); s:=floor(evalf(log10(a))+1);
for p from 1 to s do
f:=a-10*trunc(a/10); a:=trunc(a/10);
if f=0 then v[10]:=v[10]+1; else v[f]:=v[f]+1; fi;
od;
od;
end:
P(10000);
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