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 A201498 #21 Oct 30 2018 10:31:02 %S A201498 4,7,15,33,63,99,147,201,311,423,543,723,843,969,1199,1511,1743,1983, %T A201498 2313,2523,2811,3201,3611,4227,4803,5103,5409,5727,6051,7059,8193, %U A201498 8843,9387,10215,11103,11703,12639,13449,14279,15311,16023,17103,18243,18819,19407 %N A201498 a(n) = (prime(n) - 1)*(prime(n+1) - 1)/2 + 3. %C A201498 Consider strictly increasing sequence with the rule: %C A201498 a(n) is the smallest pairwise sum s of all previous terms such that s > a(n-1). %C A201498 We start with some pair of coprime positive integers b < c, a(1)=b, a(2)=c; from now on, to find a(n) we use the above-mentioned rule. We observe that, for any seeds b,c, after some term, a(n) = a(n-1) + 1. %C A201498 E.g., for b=7, c=12, we get 7, 12,1 9, 26, 31, 33, 38, 40, 43, 45, 47, 50, 52, 54, 55, 57, 59, 61, 62, 64, 66, 67, 68, 69, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, ... %C A201498 We stop at the term a(L=36) = 85 after which a(n) = a(n-1) + 1. %C A201498 In the general case of arbitrary coprime b < c, the length of the sequence is L = 3 + (b-1)(c-1)/2, and a(L) = b*c + 1. %C A201498 In A201498, we present the dependence of L(n) for the particular case b=prime(n) and c=prime(n+1). %F A201498 a(n) = A099407(n) + 3. %t A201498 #/2+3&/@(Times@@@Partition[Prime[Range[50]]-1,2,1]) (* _Harvey P. Dale_, Jun 01 2015 *) %o A201498 (PARI) p=2;forprime(q=3,1e3,print1((p-1)*(q-1)/2+3", ");p=q) \\ _Charles R Greathouse IV_, Dec 05 2011 %K A201498 nonn %O A201498 1,1 %A A201498 _Zak Seidov_, Dec 02 2011