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 A088250 #19 Mar 01 2022 09:28:41
%S A088250 1,1,2,330,10830,25410,512820,512820,12960606120,434491727670,
%T A088250 1893245380950,71023095613470,878232256181280,11429352906540438870
%N A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.
%C A088250 Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
%C A088250 Both conjectures follow from Dickson's conjecture. [_Charles R Greathouse IV_, Mar 14 2011]
%H A088250 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_379.htm">Puzzle 379. SG primes and its prime average</a>, The Prime Puzzles and Problems Connection.
%e A088250 a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
%t A088250 a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* _Giovanni Resta_, Mar 31 2017 *)
%Y A088250 Cf. A088251, A088252, A088651, A125838, A125839.
%K A088250 nonn,more
%O A088250 1,3
%A A088250 _Amarnath Murthy_, Sep 26 2003
%E A088250 Edited by _Don Reble_, Sep 29 2003
%E A088250 Entry revised by _N. J. A. Sloane_, Jan 05 2007
%E A088250 a(14) from _Giovanni Resta_, Mar 31 2017