

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
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OFFSET

2,9


LINKS

Table of n, a(n) for n=2..87.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 20122018.


EXAMPLE

P(2)/22^0=2 is prime, so a(2)=0;
P(10)/22^3=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(t2^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 * A016570 A070773 A046804
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



