Our past puzzles
838 were devoted to Kaprakar prime numbers.
In the first of these (
announced that R(19) was the first and only Kaprekar prime
number known, and invited to found more. Emmanuel Vantieghem and Jan
van Delden shown that every R(n) such that n is prime of the
form 9k+1 was Kaprekar and primes. Accordingly R(109287) and
R(270343) must be also Kaprekar prime numbers.
In the second of these (
838 ) we
invited to find more prime numbers out of the Repunits,
without giving any kind of clue. The result was that we had
not any success. Even, we received not any contribution.
Now we provide a clue, hoping
this to be a good clue.
prime Kaprekar solutions already found (the three repunits
already mentioned above) are part of the following infinite
family of Kaprekar numbers: R(n), for n=9k+1.
Are there more infinity
families of Kaprekar numbers such that at the same they are
odds and not ending in 5?
Again, by inspection of the first
51514 Kaprekar numbers computed by R.
Gerbicz and given
we found the following three of such families:
family if Kaprekar integers, odd not ending in 5,
Can you find a prime or a probable prime in some the these
infinite family of integers?
Q2. Can you
find other infinite families
for our target?