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 A103514 #42 Sep 11 2018 02:59:01
%S A103514 0,1,1,1,1,1,1,1,3,1,2,1,25,2,1,6,6,19,1,13,3,3,11,29,2,1,6,3,4,2,6,4,
%T A103514 15,6,4,20,4,1,7,16,4,7,22,3,12,13,9,35,2,3,3,52,35,3,32,15,13,10,53,
%U A103514 56,9,16,36,5,8,5,22,3,14,2,64,37,8,22,42,11,22,22,12,11,26,1,54,187,20,9
%N A103514 a(n) is the smallest m such that primorial(n)/2 - 2^m is prime.
%H A103514 R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018.
%e A103514 P(2)/2-2^0=2 is prime, so a(2)=0;
%e A103514 P(10)/2-2^3=3234846607 is Prime, so a(10)=3.
%t A103514 nmax = 2^8192; npd = 1; n = 2; npd = npd*Prime[n]; While[npd < nmax, tn = 1; tt = 2; cp = npd - tt; While[(cp > 1) && (! (PrimeQ[cp])), tn = tn + 1; tt = tt*2; cp = npd - tt]; If[cp < 2, Print["*"], Print[tn]]; n = n + 1; npd = npd*Prime[n]]
%t A103514 (* Second program: *)
%t A103514 k = 1; a = {}; Do[k = k*Prime[n]; m = 1; While[ ! PrimeQ[k - 2^m], m++ ]; Print[m]; AppendTo[a, m], {n, 2, 200}]; a (* _Artur Jasinski_, Apr 21 2008 *)
%o A103514 (PARI) a(n)=my(t=prod(i=2,n,prime(i)),m); while(!isprime(t-2^m),m++); m \\ _Charles R Greathouse IV_, Apr 28 2015
%Y A103514 Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103153, A067026, A067027, A139439, A139440, A139441, A139442, A139443, A139444, A139445, A139446, A139447, A139448, A139449, A139450, A139451, A139452, A139453, A139454, A139455, A139456, A139457, A103514.
%K A103514 nonn
%O A103514 2,9
%A A103514 _Lei Zhou_, Feb 15 2005
%E A103514 Edited by _N. J. A. Sloane_, May 16 2008 at the suggestion of _R. J. Mathar_