# [seqfan] Re: Rif: A light variation

M. F. Hasler seqfan at hasler.fr
Thu Jan 21 00:58:39 CET 2016

```On Wed, Jan 20, 2016 at 4:21 PM, <john.mason at lispa.it> wrote:

>
> A variation on Eric's theme could be (if not already present) :
> a(n) is smallest positive integer not already in a() such that a(n) + the
> sum of the digits of a(n-1) is prime. a(1)=1.
>

Nice idea, I get
1,2,3,4,7,6,5,8,9,10,12,14,18,20,11,15,13,19,21,16,22,25,24,17,23,26,29,30,28,27,32,36,34,40,33,31,37,43,46,49,48,35,39,41,38,42,47,50,54,44,45,52,60,53,51,55,57,59,65,56,62,63,58,66,61,64,69,68,75,67,70,72,74,78,82,73,79,81,80,71,89,84,77,83,86,87,88,85,76,90,92,...
which seems not yet in the OEIS.
Up to n=1000, il looks "smooth" a(1000)=879 is also the least number not
used earlier.
But then, the smallest unused number starts growing much slower than n,
e.g. at n=5000, the least unused number is only 1326,
and at n=10^4 the least unused number is 6912 (but only 58 numbers between
this one and 10^4 are not used then).
(The difference 5000-1326 is however not smaller but even a bit larger than
10^4-6912. Maybe the sequence of the "late birds" would be interesting to
look at to understand better where this sudden but then constant (?) gap of