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 A291463 #22 Mar 24 2022 19:40:43
%S A291463 2,6,10,28,22,52,34,76,138,58,186,148,82,172,282,318,118,366,268,142,
%T A291463 438,316,498,712,388,202,412,214,436,1582,508,786,274,1390,298,906,
%U A291463 942,652,1002,1038,358,1810,382,772,394,2388,2532,892,454,916,1398,478,2410
%N A291463 a(n) is the product of n-th prime number with the distance to the next prime.
%H A291463 Harvey P. Dale, <a href="/A291463/b291463.txt">Table of n, a(n) for n = 1..1000</a>
%F A291463 a(n) = prime(n)*(prime(n+1) - prime(n)).
%F A291463 a(n) = A000040(n)*A001223(n). - _Michel Marcus_, Aug 25 2017
%e A291463 For n = 6 prime(6) = 13, prime(7) = 17 the gap is 17 - 13 = 4. So 13 * 4 = 52 and 52 is the sixth term.
%t A291463 Array[With[{p = Prime@ #}, p (NextPrime[p] - p)] &, 50] (* _Michael De Vlieger_, Sep 03 2017 *)
%t A291463 Module[{nn=60,dnp},dnp=Differences[Prime[Range[nn+1]]];Times@@@Thread[ {Prime[Range[nn]],dnp}]] (* _Harvey P. Dale_, Mar 24 2022 *)
%o A291463 (PARI) forprime(p=2,200, print1(p*nextprime(p+1)-p^2, ", "))
%Y A291463 Cf. A000040, A001223, A048852.
%K A291463 nonn
%O A291463 1,1
%A A291463 _Dimitris Valianatos_, Aug 24 2017