# [seqfan] Re: Rif: A light variation

john.mason at lispa.it john.mason at lispa.it
Wed Jan 20 21:21:55 CET 2016

```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.
Is a() a permutation of the natural numbers?
John

> Il giorno 20 Jan 2016, alle ore 14:55, "M. F. Hasler" <seqfan at hasler.fr>
ha scritto:
>
>> On Wed, Jan 20, 2016 at 9:41 AM, M. F. Hasler <seqfan at hasler.fr> wrote:
>>
>> It seems that 114 is the first integer not in this sequence.
>
> Actually, the numbers which do not appear in the sequence are those
listed
> in oeis.org/A076150 : Start of 10 consecutive composite numbers.
>
> Maximilian
>
>
>>
>>> On Wed, Jan 20, 2016 at 9:16 AM, <john.mason at lispa.it> wrote:
>>>
>>> Hi
>>> with regard to "and is a permutation of the integers >0":
>>> There will be, at some time in the integers > 0, a sequence of one
hundred
>>> composite numbers.
>>> Some of these, in particular in the middle, will never give a resulting
>>> prime when added to the last (single) digit of a(n-1). Therefore they
will
>>> not be in a(n).
>>> Therefore a(n) is not a permutation of the integers > 0, and it would
be
>>> fun to find the first integer not present!
>>> john
>>>
>>>
>>>
>>>
>>> Da:     Eric Angelini <Eric.Angelini at kntv.be>
>>> Per:    Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> Data:   20/01/2016 10:57
>>> Oggetto:        [seqfan] A light variation
>>> Inviato da:     "SeqFan" <seqfan-bounces at list.seqfan.eu>
>>>
>>>
>>>
>>> Hello SeqFans,
>>> here is https://oeis.org/A055265 :
>>>
>>>> a(n) is the smallest positive integer not already in the sequence
>>>> such that a(n)+a(n-1) is prime, starting with a(1)=1.
>>>
>>> I propose this variant:
>>>
>>> E> a(n) is the smallest positive integer not already in the sequence
>>> E> such that a(n)+[the last digit of a(n-1)] is prime, starting with
>>> a(1)=1.
>>>
>>> I guess E starts like this (and is a permutation of the integers >0):
>>> E = 1,2,3,4,7,6,5,8,9,10,11,12,15,14,13,16,17,22,21,18,23,20,...
>>>
>>> Best,
>>> É.
>
>
> --
> Maximilian
>
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>
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```