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 A119488 #22 Sep 08 2022 08:45:25
%S A119488 13,23,41,83,103,89,103,113,227,229,547,373,419,263,373,787,419,433,
%T A119488 593,563,577,739,487,811,823,683,1013,599,1153,641,827,1571,1223,863,
%U A119488 883,719,1567,1187,1279,1999,1361,1373,1951,1297,2477,1091,1399,1117,2897,1459
%N A119488 Primes of the form prime(i+1)*(i+1) - prime(i)*i, for increasing values of i.
%C A119488 Some terms are repeated: e.g. 157*37 - 151*36 = 197*45 - 193*44 = 373.
%C A119488 The first numbers that are repeated 3 times are 96553, 104597, 109793, 139303, etc.
%H A119488 Harvey P. Dale, <a href="/A119488/b119488.txt">Table of n, a(n) for n = 1..1000</a>
%e A119488 The fourth prime is 7 and the third is 5.
%e A119488 Therefore 7*4 - 5*3 = 28 - 15 = 13 that is a prime.
%p A119488 P:=proc(n) local i, j; j:=ithprime(n+1)*(n+1)-ithprime(n)*n;
%p A119488 if isprime(j) then j; fi; end: a:=seq(P(i), i=1..10000);
%t A119488 Select[#[[2]] - #[[1]] &/@ Partition[Table[n Prime[n], {n, 300}], 2, 1], PrimeQ] (* _Harvey P. Dale_, Jun 05 2017 *)
%o A119488 (Magma) [m: i in [1..300] | IsPrime(m) where m is NthPrime(i+1)*(i+1)-NthPrime(i)*i]; // _Bruno Berselli_, Jun 06 2017
%Y A119488 Cf. A119487.
%K A119488 nonn,easy
%O A119488 1,1
%A A119488 _Paolo P. Lava_ and _Giorgio Balzarotti_, May 23 2006