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 A096100 #22 Oct 19 2017 10:46:16
%S A096100 1,2,2,3,6,46,1306,7695,17383720,2183805400,60512359083,447808566362,
%T A096100 181830203704703
%N A096100 a(1) = 1; for n > 1: a(n) = smallest number >1 such that product of any two or more successive terms + 1 is prime.
%C A096100 a(14) > 2.5*10^14, if it exists. - _Don Reble_, Nov 22 2015
%C A096100 So far, up through a(13), the sequence is nondecreasing. I don't know a good reason why it should stay that way. (But since candidates for each successive value get rarer, the least candidate will tend to increase.) - _Don Reble_, Nov 22 2015
%C A096100 I don't think it will be easy to prove that this sequence is nondecreasing. The analogous sequence with other starting values often leads to non-monotonic sequences, e.g., (3, 2, 2, 3, 26, 876, 15136, ...), (4, 3, 6, 6, 5, 14, 3597, 1218704, ...), or (5, 2, 3, 2, 3, 1176, 40, 142863, ...). - _M. F. Hasler_, Nov 24 2015
%e A096100 a(4) is not 2 since 2*2*2 + 1 = 9 is composite, but 2*3 + 1 = 7, 2*2*3 + 1 = 13, 1*2*2*3 + 1 = 13 are all prime, hence a(4) = 3.
%o A096100 (PARI) A096100(n, show=0, a=[1])={for(n=1, n-1, show&&print1(a[n]", "); for(k=2, 9e9, my(p=1); for(i=0,n-1,isprime(1+k*p*=a[n-i])||next(2)); a=concat(a,k); break)); a[n]} \\ Use 2nd or 3rd optional arg to print intermediate terms or to use other starting value(s) of the sequence. Not efficient enough to go beyond a(8). - _M. F. Hasler_, Nov 24 2015
%K A096100 more,nonn
%O A096100 1,2
%A A096100 _Amarnath Murthy_, Jun 24 2004
%E A096100 Edited, corrected and extended by _Klaus Brockhaus_, Jul 05 2004
%E A096100 a(10) from _Donovan Johnson_, Apr 22 2008
%E A096100 a(11)-a(13) from _Don Reble_, Nov 22 2015