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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
OFFSET
2,9
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
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