[seqfan] Re: Any digit-pair in S sums to a prime

[Maximilian Hasler]

Dear all,
I forgot to mention that both variants of the "sum" version had
already been proposed almost exactly 1 year ago,
cf. A182175, A182177, A182178 and
http://list.seqfan.eu/pipermail/seqfan/2012-April/009403.html
where variants had been proposed by using other sets than
{2,3,5,7,11,13,17} for allowed resp. forbidden digit sums.

The "abs.diff." versions are now proposed as
A219249,A219250,
and the numbers missing in A182177, A182178 are in
A219110
(while the "candidates for extending A182177, A182178" are in A182175).

Maximilian


On Thu, Apr 11, 2013 at 11:46 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> Many thanks to Lars and Maximilian -- this is now here, with a nice
> graph:
> http://www.cetteadressecomportecinquantesignes.com/AnyDigitPair.htm
> Best,
> É.
>
>
>
>
> -----Message d'origine-----
> De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de Maximilian Hasler
> Envoyé : jeudi 11 avril 2013 16:39
> À : Sequence Fanatics Discussion list
> Objet : [seqfan] Re: Any digit-pair in S sums to a prime
>
> On Wed, Apr 10, 2013 at 6:57 PM, Eric Angelini wrote:
>>
>> Any digit-pair in S sums to a prime, commas or not:
>> S=1,2,3,4,7,6,5,8,9,20,21,11,12,14,16,50,23,25,29,41,43,47,49,83,85,61,65,
>>
>
> I think "any 2 subsequent digits" would be better,
> "any pair" does not require that they are neighbors.
>
>> S is supposed not to show twice the same
>> integer, and S wants to be the lexicofirst such seq.
>>
>
> The sequence
> 0, 2, 1, 4, 3, 8, 5, 6, 7, 41, 11, 12, 9, 20, 21, 14, 16, 50, 23, ...
> has the same property and is lexicographically smaller than yours. ;-)
>
> My script
>
> EA114(n,a=[1],u=0)={ while(#a<n, u+=1<<a[#a];
>  for(t=a[1]+1,9e9, bittest(u,t) & next; my(d=concat(a[#a]%10,digits(t)));
>  for(i=2,#d, isprime(d[i-1]+d[i]) || next(2)); a=concat(a,t);break));a }
>
> confirms your terms (if they are to be positive).
>
>
>> The same seq with prime absolute
>> differences between digits is perhaps T:
>>
>> T=1,3,5,2,4,6,8,13,14,7,9,20,24,16,18,30,25,27,29,41,31,35,36,38,50,52,42,46,
>> 47,49,61,63,53,57,58,64,68,69,70,72,74,75,79,202,92,94,96,81,83,85,86,97,
>> 203,130,205,207,241,302,413,131,...
>>
>
> Here, too, my script
>
> EA114b(n,a=[1],u=0)={ while(#a<n, u+=1<<a[#a];
>  for(t=a[1]+1,9e9, bittest(u,t) & next; my(d=concat(a[#a]%10,digits(t)));
>  for(i=2,#d, isprime(abs(d[i-1]-d[i])) || next(2)); a=concat(a,t);break));a }
>
> Confirms your terms if they are to be positive, and else yields
>
> 0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 13, 14, 16, 18, 30, 20, 24, 25, 27, 29,
> 41, 31, 35, 36, 38, 50, 52, 42, 46, 47, 49, 61, 63, 53, 57, 58, 64,
> 68, 69, 70, 72, 74, 75, 79, 202, 92, 94, 96, 81, 83,...
>
>
> A related sequence would be that of numbers which certainly will never
> be in any of these sequences, like 10,13,15,17,18,19,22,24,...
> which is not yet on OEIS, and between 10 and 100 close to
> A104211                 Integers n such that the sum of the digits of n is not prime.
>
> Best wishes,
> Maximilian
>
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