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.
%I A288819 #21 Jul 31 2017 12:57:37
%S A288819 0,1,3,4,5,6,8,12,13,17,18,21,22,23,25,30,34,41,45,54,58,60,62,66,75,
%T A288819 80,82,83,88,104,110,124,131,147,163,166,173,194,220,228,233,257,290,
%U A288819 313,334,350,359,365,412,468,477,503,520
%N A288819 Record maxima in A288818.
%C A288819 If one assumes that larger records occur at A288818 indices beginning with 22 or 23, then a(54)-a(64) are: 528, 534, 538, 542, 636, 657, 687, 728, 764, 768, and 847. - _Hans Havermann_, Jul 31 2017
%t A288819 ric[d_, lp_] := Block[{p, e, i, j, n = Length@d}, If[n == 0, cnt++, If[d[[1]] > 0, Do[p = FromDigits@ Take[d, i]; If[p > lp && PrimeQ@p, ric[Take[d, i - n], p]; Do[e = Take[d, {i + 1, j}]; If[e[[1]] > 0 && e != {1}, ric[Take[d, j - n], p]], {j, i+1, n}]], {i, n}]]]]; a[n_] := (cnt = 0; ric[ IntegerDigits@ n, 1]; cnt); Union@ FoldList[Max, Array[a, 10^6]] (* _Michael De Vlieger_, Jun 19 2017, after _Giovanni Resta_ at A288818 *)
%Y A288819 Cf. A288818, A288820 (records' position), A080670.
%K A288819 nonn,base,more
%O A288819 1,3
%A A288819 _Hans Havermann_, Jun 17 2017
%E A288819 a(46)-a(53) from _Giovanni Resta_, Jun 20 2017