|
%I #42 Sep 11 2018 02:59:01
%S 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 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 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 a(n) is the smallest m such that primorial(n)/2 - 2^m is prime.
%H 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 P(2)/2-2^0=2 is prime, so a(2)=0;
%e P(10)/2-2^3=3234846607 is Prime, so a(10)=3.
%t 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 (* Second program: *)
%t 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 (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 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 nonn
%O 2,9
%A _Lei Zhou_, Feb 15 2005
%E Edited by _N. J. A. Sloane_, May 16 2008 at the suggestion of _R. J. Mathar_
|
