[seqfan] Rif: Re: Rif: A light variation

[john.mason at lispa.it]

Following Maximilian's idea of looking at the late birds, I generated the 
sequence through 10^5 terms.
Here are the first 18 late birds, that is numbers not present in the 
sequence.
After each one I show the number of composites. These high numbers, higher 
than the digit sum of 99999, are a hindrance to the late birds being 
picked. 
An exception is 25470 which is followed by a prime, and then 51 
composites. But until the term 100000 itself is included in the sequence, 
we won't have a number with a digit sum of 1.
john


missing 19609 followers 51
missing 19610 followers 50
missing 19611 followers 49
missing 19612 followers 48
missing 19613 followers 47
missing 19614 followers 46
missing 19615 followers 45
missing 19616 followers 44
missing 25470 followers 0 51
missing 25471 followers 51
missing 25472 followers 50
missing 25473 followers 49
missing 25474 followers 48
missing 25475 followers 47
missing 25476 followers 46
missing 25477 followers 45
missing 25478 followers 44
missing 28228 followers 0 47




Da:     "M. F. Hasler" <seqfan at hasler.fr>
Per:    Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Data:   21/01/2016 00:59
Oggetto:        [seqfan] Re: Rif: A light variation
Inviato da:     "SeqFan" <seqfan-bounces at list.seqfan.eu>



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

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