%I #11 Jan 12 2022 18:09:39
%S 1,2,3,4,7,9,10,11,12,13,14,15,16,20,21,23,26,27,30,35,36,37,39,40,43,
%T 53,55,67,72,85,97,98,123,130,131,132,138,141,146,180,182,185,188,192,
%U 201,225,231,236,240,248,252,254,276,300,322,326,346,372,401,413,424
%N a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) + 1 or a(1)*a(2)*...*a(n) - 1 is prime.
%H Iain Fox, <a href="/A172024/b172024.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="http://www.primecurios.com">Prime Curios!</a>
%t For[n = 2; res = {1}; z = 1, n <= 1000, n++, If[PrimeQ[n z + 1] || PrimeQ[n z - 1], AppendTo[res, n]; z *= n]] res (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 28 2010 *)
%t nxt[{prd_,a_}]:=Module[{c=a+1},While[ NoneTrue[prd*c+{1,-1},PrimeQ],c++];{prd*c,c}]; NestList[nxt,{1,1},60][[All,2]] (* _Harvey P. Dale_, Jan 12 2022 *)
%o (PARI) first(n) = { my(res = vector(n), p=1); res[1]=1; for(x=2, n, my(k=res[x-1]+1); while(!ispseudoprime(p*k+1) && !ispseudoprime(p*k-1), k++); res[x]=k; p*=k); res; } \\ _Iain Fox_, Nov 30 2017
%K nonn
%O 1,2
%A _G. L. Honaker, Jr._, Jan 22 2010
%E Terms beyond a(15) from _R. J. Mathar_ and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010