# Primes with Lucas number digital root (or primitive root)

Jonathan Post jvospost3 at gmail.com
Wed Jun 25 17:12:54 CEST 2008

```Primes with Lucas number digital root.

This is to A000032 as A003147 is to A000045.

A001122 Primes with primitive root 2 UNION A001123 Primes with 3 as
smallest primitive root UNION A001126  Primes with 7 as smallest
primitive root.  UNION A019339  Primes with primitive root 11 UNION
A019345  Primes with primitive root 18. UNION...

Hold on -- A001123 should be replaced with A019334  Primes with
primitive root 3.
And A001126 by A019337  Primes with primitive root 7.

Or maybe it's better to just list the complement?

Now I'm worried that I confused digital root with primitve root.
[throws up hands, looks to seqfans for signs of interest]

Is there a sequence in here worth digging out?

On Jun 25, 2008, at 9:45 AM, Eric Angelini wrote:

> Could please someone compute a few terms more of:
> < Add to n the n-th smallest number not dividing n >
> I've found this first few terms:
> S = 1,3,8,20,46,96,...

I think each term is twice the previous term plus the number of
divisors of the previous term:

{1, 3, 8, 20, 46, 96, 204, 420, 864, 1752, 3520, 7068, 14160, 28360,
56736, 113508, 227040, 454176, 908424, 1816944, 3633908, 7267828,
14535662, 29071328, 58142704, 116285418, 232570884, 465141864,
930283760, 1860567600, 3721135320, 7442270736, 14884541492,
29769083008, 59538166080, 119076332272, 238152664554, 476305329172,
952610658350, 1905221316724, 3810442633460, 7620885266932,
15241770533876, 30483541067764, 60967082135576, 121934164271216,
243868328542452, 487736657084916, 975473314169850, 1950946628339784,
3901893256679600, ...}

```

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