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 A073629 #8 May 03 2023 12:33:19
%S A073629 1,2,3,5,7,8,9,13,17,20,21,25,31,32,39,47,49,56,59,63,73,74,83,87,93,
%T A073629 96,97,103,105,114,117,121,127,134,139,141,143,146,147,151,155,160,
%U A073629 165,167,169,172,175,185,187,192,193,197,205,214,223,235,239,240,253,259,261
%N A073629 a(1) = 1; a(2) =2; a(3) = 3; a(n) = smallest number greater than the previous term such that the sum of four successive terms is a prime.
%e A073629 a(4)=5 as 1+2+3+5=11 is prime, 1+2+3+4=10 composite
%t A073629 nxt[{a_,b_,c_}]:=Module[{k=c+1},While[!PrimeQ[a+b+c+k],k++];{b,c,k}]; Transpose[NestList[ nxt[#]&,{1,2,3},70]][[1]] (* _Harvey P. Dale_, Aug 29 2012 *)
%Y A073629 Cf. A073627, A073628.
%K A073629 nonn
%O A073629 1,2
%A A073629 _Amarnath Murthy_, Aug 08 2002
%E A073629 Corrected and extended by _Sam Alexander_, Feb 26 2005