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 192113, we say: one 3's, three 1's, one 2's, one 9's, so 13311219
The term after 1411 is obtained by saying "two 1's, one 4, one 1", which gives 211411.
The term after 1711 is obtained by saying "two 1's, one 7, one 1", which gives 211711.
NestList[FromDigits@ Flatten@ Map[Reverse@ Flatten@ Tally[#] &, Split@ Reverse@ IntegerDigits[#]] &, 7, 9] (* Michael De Vlieger, Dec 16 2021 *)
E.g., the term after 1811 is obtained by saying "two 1's, one 8, one 1", which gives 211811.
split[n_]:=Split[Reverse[IntegerDigits[n]]];
list1[n_]:=List/@Length/@split[n];riffle1[n_]:=Riffle[split[n],list1[n]];
tab[n_]:=Table[i,{i,1,2*Length[list1[n]],2}];
list2[n_]:=Append[riffle1[n][[#]],riffle1[n][[#+1]]]&/@tab[n];
flat[n_]:=Flatten/@list2[n];riffle2[n_]:=Riffle[Last/@flat[n],First/@flat[n]];
a[1]=8; a[n_]:=FromDigits[riffle2[a[n-1]]]; Array[a,10] (* or *)
IntegerReverse[NestList[FromDigits[Flatten[Replace[Replace[Replace[Split[Reverse[IntegerDigits[#]]],{x_,y_}->{x,Length[{x,y}]},{1}],{x_,y_,z_}->{x,Length[{x,y,z}]},{1}],{x_}->{x,Length[{x}]},{1}]]]&,8,9]] (* Ivan N. Ianakiev, Nov 10 2016 *)
71, 331 and 1277, for instance, belong to the sequence because their respective descriptions 1171 (one 1, one 7), 1123 (one 1, two 3's) and 271211 (two 7's, one 2, one 1) are primes.
LookAndSayA[ n_] := FromDigits@Flatten@((Through[ {Length, First}[ # ] ] &) /@ Split@Reverse@IntegerDigits@n); Select[Prime@Range[450],PrimeQ@LookAndSayA@# &] (* Ray Chandler, Jan 16 2007 *)
To get the term after 211312, we say: two 2's, three 1's, one 3's, so 223113.
To get the term after 122113, we say: one 3's, three 1's, two 2's, so 133122
To get the term after 112213, we say: one 3's, three 1's, two 2's, so 133122
To get the term after 142113, we say: one 3's, three 1's, one 2's, one 4's, so 13311214
To get the term after 152113, we say: one 3's, three 1's, one 2's, one 5's, so 13311215
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