[seqfan] Sum of the cubes of the digits plus the prime equal the prime squared

[Charles Greathouse]

Sequence fans, Will  Gosnell asked me to forward this message to the list.
He's trying to add a sequence based on a short list of triples. I believe
he wants computational assistance with his problem and also I think he's
not sure what is the best way to format them as a sequence.

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Dear  Sequence fan list,  I have 5 sequences on Oeis at present . Charles
Greathouse  suggested I email you  with the information for this new
sequence submission I have and that you could be of some assistance in
having the sequence added to OEIS under my name Gosnell.  This sequence is
a subsequence of the  sequence that starts  with the prime 17  on my page
.  I told   Charles that I only  have  4 examples at present  which appear
in the first 10 thousand terms  in the sequence that starts with 17 on my
OEIS page.

These  prime triples  have the property that the sum of the cubes of their
digits  plus the prime all equal the same prime number squared .  The first
example is ,  242377994591  and 242377994843   and  242377995323.  So when
you add the  cubes of the digits of these primes and then add the prime
itself to that quantity  you get  the prime  492319^2  .    The second
example is    2014665131807   and  2014665132503   and 2014665132521  .
The root of these  3  is  1419389^2.   The  next example  is  3928629229589
 and  3928230693  and  3928629230783 . The root of these  is  1982077^2  .
The next  example is  5027133481449  and 5027133482069   and  5027133482159
 . the root of these  is 2242127^2.

Professor  Robert Israel at UBC  is aware of this  sequence   and  confirms
  my  belief that there are many more if not an infinite number of these
prime triples  in existence . Can you help get this  sequence of prime
 triples  added to the OEIS?

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I've been very busy lately (apologies for my absence, I have been caring
for my 6-month old daughter and my wife, and also changing jobs) but I
figure someone can probably find a good way to compute these.

Charles Greathouse
Path Robotics