# [seqfan] Re: ARB integers

M. F. Hasler oeis at hasler.fr
Sun Oct 12 15:32:08 CEST 2014

```Eric,
I wrote a simple script to check whether n = ARB and return the first
possible such decomposition.
I propose your sequence as OEIS entry https://oeis.org/draft/A248711
Unfortunately, the 3 digit terms (and maybe most of the 4-digit terms)
are not that interesting,
most are somehow trivial with B and/or R equal to 0,
maybe it would be more interesting to exclude these.
(Fun fact: the terms between 100 and 200 which do not contain th digit
0 are exactly those which are also in
A112651=Numbers n such that n^2 squared is congruent to n (mod 11).)

Best,
M.
(PARI)
isARB(n)={d=#digits(n);forvec(s=vector(2,i,[1,d-1]),
(10^s>10*B=n%10^s)&& s>1 &&next;
(10^s>10*R=n%10^s)&& s>s+1 &&next;
setsearch(Set([B+A=n\10^s,A-B,A*B,if(B,A/B)]),R\10^s)&&return([A,R\10^s,B]),2)}

On Sat, Oct 11, 2014 at 4:40 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> I'm looking for a list of integers I've lost...
> Integers of the form ARB where:
> - A, R and B are strings of digits;
> - A, R and B have no leading zero;
> - R (for 'result') can be replaced by
> one of those 4 signs [+,-,x,:] (that is:
> plus, minus, multiply, divide), such that
> the operation A op B = R.
>
> Examples of sound integers:
> ARB = 3155 because 3x5=15 (R=15)
> ARB = 100 because 1x0=0 (R=0)
> ARB = 101 because 1-1=0 (R=0)
> ARB = 110 because 1+0=1 (R=1)
> ARB = 1722113 because 17x13=221 (R=221)
> ARB = 19118 because 19-8=11 (R=11) or 19-18=1 (R=1)
> ARB = 19119 because 19:19=1 (R=1)

```