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 A111908 #14 Jun 04 2024 14:24:43
%S A111908 1,2,7,36,61,105,171,210,211,216,325,351,406,528,561,630,741,780,990,
%T A111908 1081,1176,1275,1596,1711,1830,1953,2016,2145,2346,2628,2775,3003,
%U A111908 3081,3240,3321,3655,3741,3916,4278,4371,4465,4560,4851,5253,5460,5565,5886
%N A111908 Numbers that are not the sum of a prime and a nonzero triangular number.
%C A111908 Can anybody prove or disprove a(n) = O(n^c) for some constant c?
%C A111908 _Jonathan Vos Post_ has observed that every term in A076768 also occurs in this sequence.
%H A111908 Donovan Johnson, <a href="/A111908/b111908.txt">Table of n, a(n) for n = 1..10000</a>
%e A111908 7 = 1+6 = 2+5 = 3+4; 7 is in the sequence because there is no sum where the first element is a prime and the second one a triangular number.
%t A111908 lim=6000;plim=PrimePi[lim];tlim=Ceiling[Sqrt[2lim]];Complement[Range[lim],Union[Flatten[Table[Prime[i]+PolygonalNumber[j],{i,plim},{j,tlim}]]]] (* _James C. McMahon_, Jun 04 2024 *)
%Y A111908 Cf. A064233, A000217, A076768, A020756, A072386, A014089, A014090, A000404, A001481, A002654, A100570, A101181.
%K A111908 nonn
%O A111908 1,2
%A A111908 _Stefan Steinerberger_, Nov 25 2005
%E A111908 a(47) and offset corrected by _Donovan Johnson_, Feb 09 2013