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 A103514 a(n) is the smallest m such that primorial(n)/2 - 2^m is prime. 24
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,9 LINKS R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. EXAMPLE P(2)/2-2^0=2 is prime, so a(2)=0; P(10)/2-2^3=3234846607 is Prime, so a(10)=3. MATHEMATICA 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]] (* Second program: *) 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 *) PROG (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 CROSSREFS 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. Sequence in context: A321889 A321751 A188584 * A324123 A016570 A070773 Adjacent sequences:  A103511 A103512 A103513 * A103515 A103516 A103517 KEYWORD nonn AUTHOR Lei Zhou, Feb 15 2005 EXTENSIONS Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified October 18 10:05 EDT 2019. Contains 328146 sequences. (Running on oeis4.)