# [seqfan] Any digit of F is the sum of two other digits of F

Eric Angelini Eric.Angelini at kntv.be
Mon Jan 2 01:14:25 CET 2012

```HNY to everyone!
And here is our first 2012 seq proposition:
Integers F having all of their digits
being the sum of two other F digits:
F(n)=
10001, 10010, 10100, 11000, 20002,
20020, 20200, 22000, 30003, 30030,
30300, 33000, 40004, 40040, 40400,
44000, 50005, 50050, 50500, 55000,
60006, 60060, 60600, 66000, 70007,
70070, 70700, 77000, 80008, 80080,
80800, 88000, 90009, 90090, 90900,
99000, 100001, 100010, 100011, 100012, 100021, ...

I like 100012345 as this integer is
(I think) the smallest one showing
this property AND the smallest one
which, embedded in any string of
digits, will trasform this string of
digits into a member of F.

Example (for 100012345):
- any digit "1" is the sum of one of
the three "0"s and the other "1";
- any digit "0" is the sum of the
two other "0"s;
- the digit "2" is the sum of the
two digits "1";
- the digit "3" is the sum of the
digits "1" and "2";
- the digit "4" is the sum of the
digits "1" and "3";
- the digit "5" is the sum of the
digits "2" and "3".

Now if you embed 100012345
inside, say, 6789 like this:
"6710001234589" you will see
that this new integer is a F number.
Let's check:
- the digit "6" is the sum of the
digits "2" and "4";
- the digit "7" is the sum of the
digits "3" and "4";
- the digit "8" is the sum of the
digits "3" and "5";
- the digit "9" is the sum of the
digits "4" and "5".
The other digits have been checked
before.

We thus see that "6710001234589"
is indeed a number F having all
of its digits being the sum of two
other digits of F.

Which would be the seq of the
prime numbers of F?

Best,
É.

```