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.
f[n_] := Product[Prime[k + n], {k, n}] - Product[Prime[k], {k, n}]; Table[ f[n], {n, 0, 14}] (* Robert G. Wilson v, Jun 14 2005 *)
Triangle begins:
1;
2, 1;
6, 3, 1;
30, 15, 5, 1;
210, 105, 35, 7, 1;
...
T:= proc(n, k) option remember;
`if`(n=k, 1, T(n-1, k)*ithprime(n))
end:
seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Jan 21 2022
T[n_, k_] := Times @@ Prime[Range[k + 1, n]];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 13 2021 *)
pr(n) = factorback(primes(n)); \\ A002110 row(n) = my(P=pr(n)); vector(n+1, k, P/pr(k-1)); \\ Michel Marcus, Jan 21 2022
a(5) = 2803043 because 2*3*5*7*11 + 13*17*19*23*29 = 2803043.
a:= n-> add(mul(ithprime(i+j), i=1..n), j=[0, n]): seq(a(n), n=0..20); # Alois P. Heinz, Apr 13 2024
690 is OK because prime(690)-690 = 5179-690 = 4489 = 67^2, 67 is prime.
lst = {}; fQ[n_] := Block[{pf=FactorInteger[n]}, (2-Length[pf])(pf[[1, 2]]-1) > 0]; Do[ If[ fQ[Prime[n] - n], Print[n]; AppendTo[lst, n]], {n, 3, 362439}]; lst
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