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 A362888 #6 May 20 2023 16:09:38
%S A362888 1,252,2310152797,28410981127871160285705816883937448685
%N A362888 a(1) = 1, a(n) = (3*k + 1)*(6*k + 1)*(8*k + 1), where k = Product_{i=1..n-1} a(i).
%C A362888 A sequence of pairwise relatively prime hexagonal pyramidal numbers. Its infinitude implies, by the Fundamental theorem of arithmetic, the infinitude of primes.
%C A362888 Building on an idea by Sierpinsky (see References): For m > 5, the general term of the sequence of m-gonal pyramidal numbers is a(n) = n*(n+1)*((m-2)*n - (m-5))/6. Therefore, for m > 5, there are infinitely many sequences of pairwise relatively prime m-gonal pyramidal numbers, with first term any positive m-gonal pyramidal
%C A362888 number and general term of the form a(n) = (3*k + 1)*(6*k + 1)*(2*k*(m - 2) + 1), where k = Product_{i=1..n-1} a(i). Corollary: There are infinitely many sequences of m-gonal pyramidal numbers to base the proof of the infinitude of primes on.
%D A362888 W. Sierpinski, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970. Problem #43.
%F A362888 a(1) = 1, a(n) = (3*k + 1)*(6*k + 1)*(8*k + 1), where k = Product_{i=1..n-1} a(i).
%t A362888 a[1]=1; a[n_]:=Module[{k=Product[a[i],{i,1,n-1}]},(3*k+1)*(6*k+1)*(8*k+1)];
%t A362888 a/@Range[5]
%Y A362888 Cf. A002412, A360826.
%K A362888 nonn
%O A362888 1,2
%A A362888 _Ivan N. Ianakiev_, May 08 2023