[seqfan] Re: Shortest sequence to get prime

[Neil Fernandez]

In message <bNBr5oA1IdNdFw1O at borve.org>, Neil Fernandez
<primeness at borve.org> writes
>Hi again Alonso,
>
>Another sequence we can make is
>
>a(n):= smallest odd prime p for which np is the smallest multiple of p
>such that np-1 is square-free
>
>This begins 3, 17, 5, 113, 4019, 6701, 84317, 1284817, 39957487, ...
>
>3     (3*1 - 1    = 2),
>17    (17*2 - 1   = 3 * 11),
>5     (5*3 - 1    = 2 * 7),
>113   (113*4 - 1  = 11 * 41),
>4019  (4019*5 - 1 = 2 * 3 * 17 * 97),
>6701  (6701*6 - 1 = 5 * 11 * 17 * 43),
>84317 (84317*7 - 1       = 2 * 43 * 6863),
>1284817 (1294817*8 - 1   = 3 * 5 * 11 * 67 * 937),
>39957487 (39957487*9 - 1 = 2 * 223 * 806317),

It is easy to see that for odd n, n*a(n)-1 is divisible by 2; but is it
a coincidence that for the first four even values of n, n*a(n)-1 is
divisible by 11?

Neil 

-- 
Neil Fernandez