[seqfan] Re: 10-digit accepting integers

M. F. Hasler seqfan at hasler.fr
Mon Oct 27 22:54:37 CET 2014

```Eric,

I think the list of such numbers starts 411203, 411205, 4111203,
4111205, 4112023, 4112025,...,
e.g. for 411203 :
411203[0], 41[1]1203, 41[2]1203, 4112[3]03, 41[4]1203, 4112[5]03,
41[6]1203, [7]411203, 411203[8], [9]411203.

PS: Funny enough, in your oldest post you considered 41123 - you were
just a 0 away from the solution!

--
Maximilian

(PARI)
/*possible neighbors*/pn=vector(10,n,select(t->isprime(t+n-1),vector(10,i,i-1)))
/*The following is "buggy" because it would e.g. accept "0" as prefix
to a number starting with a prime digit.
But results are OK for numbers not starting with prime digits or
ending in a prime digit or having two neighboring prime digits.*/
{can_accept_all(n)=d=digits(n);!for(D=0,9,setsearch(pn[d[1]+1],D)&&next;setsearch(pn[d[#d]+1],D)&&next;
for(i=3,#d-1,(t=setintersect(pn[d[i-1]+1],pn[d[i]+1]))&&setsearch(t,D)&&next(2));return)}
is_A182175(n)=!for(i=2, #n=digits(n), isprime(n[i-1]+n[i])||return)

On Mon, Oct 27, 2014 at 12:12 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello Seqfans,
> There is an infinity of such 10-digit accepting numbers!
>
> Take 43021123 for instance (where 2 adjacent digits sum to 7,3,2,3,2,3,5 = primes)
>
> 43021123 + 0 = 430211230 -- Two adjacent digits sums = 7,3,2,3,2,3,5,3
> 43021123 + 1 = 143021123 -- Two adjacent digits sums = 5,7,3,2,3,2,3,5
> 43021123 + 2 = 430211232 -- Two adjacent digits sums = 7,3,2,3,2,3,5,5
> 43021123 + 3 = 343021123 -- Two adjacent digits sums = 7,7,3,2,3,2,3,5
> 43021123 + 4 = 430211234 -- Two adjacent digits sums = 7,3,2,3,2,3,5,7
> 43021123 + 5 = 430521123 -- Two adjacent digits sums = 7,3,5,7,3,2,3,5
> 43021123 + 6 = 430216123 -- Two adjacent digits sums = 7,3,2,3,7,7,3,5
> 43021123 + 7 = 743021123 -- Two adjacent digits sums = 11,7,3,2,3,2,3,5
> 43021123 + 8 = 430211238 -- Two adjacent digits sums = 7,3,2,3,2,3,5,11
> 43021123 + 9 = 943021123 -- Two adjacent digits sums = 13,7,3,2,3,2,3,5
>
> 43021123 produces immediately a family of 10-digit accepting integers
> by simply expanding the "11" pattern into "111", "1111", 111...111":
>
> 43021123, 430211123, 4302111123, 4302111...11123
>
> The question of the smallest such 10-digit accepting integer is still open.
> Best,
> É.
>
>
> -----Message d'origine-----
> De : SeqFan [mailto:seqfan-bounces at list.seqfan.eu] De la part de Eric Angelini
> Envoyé : lundi 27 octobre 2014 12:53
> À : Sequence Fanatics Discussion list
> Objet : [seqfan] 9-digit accepting integers
>
> Hello SeqFans,
> 21123 has the property that every pair of adjacent digits sum to a prime number
> (thus belonging to https://oeis.org/A182175).

```