[seqfan] Re: Rif: A light variation

[Zak Seidov]

 Another  variation:
a(n) is the 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.


>Среда, 20 января 2016, 19:58 -04:00 от "M. F. Hasler" <seqfan at hasler.fr>:
>
>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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