[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
about 3000 comes from.)

Is a() a permutation of the natural numbers?
>

In spite of what precedes, my wild guess (not to say conjecture) would be
"yes".

Maximilian


More information about the SeqFan mailing list