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 A038771 #44 Jan 07 2019 03:50:15
%S A038771 4,9,25,49,121,221,289,529,667,899,1147,1591,2021,1849,2773,3551,4087,
%T A038771 4819,4757,5041,7519,7663,8549,9991,10379,13231,11227,14659,11881,
%U A038771 21877,25283,18209,22331,20989,22499,25591,27221,29503,31313,34547
%N A038771 a(n) is the smallest composite number c such that A002110(n) + c is prime.
%C A038771 The lower "envelope" of the sequence is prime(n+1)^2. See also Fortune-conjecture (A005235).
%C A038771 For some n, c=prime(n+1)^2; for others, it is larger, even not necessarily divisible by prime(n+1). E.g., at n=11, prime(11)=31 and a(11) = 1591 = 37*43 = prime(12)*prime(14), while for n=59, a(59) = 97969 = 313^2 = prime(65)^2, etc. Adding these to the suitable primorial numbers, primes are obtained.
%C A038771 Conjecture: lim inf_{n->oo} a(n)/prime(n+1)^2 = 1 < lim sup_{n->oo} a(n)/prime(n+1)^2 = 2. - _Charles R Greathouse IV_ and _Thomas Ordowski_, Apr 24 2015
%C A038771 Conjecture: all the terms in this sequence have exactly two prime factors. This conjecture is true for the first 133 terms. - _Dmitry Kamenetsky_, Jan 06 2019
%H A038771 Dmitry Kamenetsky, <a href="/A038771/b038771.txt">Table of n, a(n) for n = 0..133</a>
%o A038771 (PARI) a(n) = {my(q = prod(i=1, n, prime(i))); forcomposite(c = 1,, if (isprime(q+c), return(c);););} \\ _Michel Marcus_, May 24 2015
%Y A038771 Cf. A002110, A054757, A054758, A005235.
%K A038771 nonn
%O A038771 0,1
%A A038771 _Labos Elemer_, May 04 2000
%E A038771 Name edited by _Tom Edgar_, Jun 08 2015
%E A038771 a(0) prepended by _Dmitry Kamenetsky_, Jan 06 2019