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A359940 Lexicographically earliest sequence of distinct primes whose partial products lie between noncomposite numbers.

%I A359940 #12 Jan 21 2023 03:27:38
%S A359940 2,3,5,19,11,7,31,23,193,67,367,131,317,1097,241,1777,773,2819,2689,
%T A359940 1381,1741,3389,631,8581,41,1553,2297,1427,17053,1493,883,619,9803,
%U A359940 13331,26203,37,7681,41269,1913,27091,3079,31583,5867,22409,13367,37337,29573,6469
%N A359940 Lexicographically earliest sequence of distinct primes whose partial products lie between noncomposite numbers.
%H A359940 Amiram Eldar, <a href="/A359940/b359940.txt">Table of n, a(n) for n = 1..230</a>
%e A359940 2 - 1 = 1 and 2 + 1 = 3 are both noncomposite numbers.
%e A359940 2*3 - 1 = 5 and 2*3 + 1 = 7 are both noncomposite numbers.
%e A359940 2*3*5 - 1 = 29 and 2*3*5 + 1 = 31 are both noncomposite numbers.
%p A359940 P:= {seq(ithprime(i),i=2..10^5)}:
%p A359940 R:= 2: s:= 2:
%p A359940 for i from 2 to 100 do
%p A359940   found:= false;
%p A359940   for p in P do
%p A359940     if isprime(p*s-1) and isprime(p*s+1) then R:= R,p; s:= p*s; P:= P minus {p}; found:= true; break fi;
%p A359940   od;
%p A359940   if not found then break fi
%p A359940 od:
%p A359940 R; # _Robert Israel_, Jan 19 2023
%t A359940 a[1] = 2; a[n_] := a[n] = Module[{t = Table[a[k], {k, 1, n - 1}], p = 2, r}, r = Times @@ t; While[MemberQ[t, p] || ! PrimeQ[r*p - 1] || ! PrimeQ[r*p + 1], p = NextPrime[p]]; p]; Array[a, 50]
%Y A359940 Cf. A008578, A014574, A083771, A167777, A290427, A359939.
%K A359940 nonn
%O A359940 1,1
%A A359940 _Amiram Eldar_, Jan 19 2023