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 A268495 #5 Feb 09 2016 20:54:14
%S A268495 0,1,3,5,6,11,14,17,26,61,62,74,77,80,101,179,191,206,209,212,269,329,
%T A268495 341,383,401,404,425,455,458,461,467,491,557,560,581,605,614,668,680,
%U A268495 731,734,824,869,875,890,893,911,923,935,944,959,1031,1064,1097,1118,1130,1151,1154,1316,1322,1328,1349
%N A268495 "Late birds" (a(n)<a(k) for all k>n) in A268630 (= a(n)^2+a(n+1) is prime).
%C A268495 See A268494 for the corresponding indices, A268496-A268497 for records. We use offset 0 here because the first term has a special status (it's not really "late") and also because all related sequences (A268630 and A268494 - A268497) have a(0)=0 and omitting this term yields the corresponding "positive integer" variant.
%C A268495 Assuming that A268630 is a permutation of the nonnegative integers N (as conjectured), the characterization given in the name is equivalent to say that a(n) equals the least number not occurring earlier. The sequence defined that way is finite if and only if A268630 is not a permutation of N.
%H A268495 M. F. Hasler, <a href="/A268495/b268495.txt">Table of n, a(n) for n = 0..428</a>
%o A268495 (PARI) show(n,f="/tmp/b268495.txt",c=0,a=0,u=[a-1])={for(n=1, n, a==u[1]+1&&if(f,write(f,c++-1," "a),print1(a",")); u=setunion(u,[a]); while(#u>1&&u[2]==u[1]+1,u=u[^1]); for(k=u[1]+1, 9e9, !setsearch(u, k) && isprime(a*a+k) && (a=k) && break))}
%K A268495 nonn
%O A268495 0,3
%A A268495 _M. F. Hasler_, Feb 09 2016