Triple Double
For those of you who know basketball, you will be familiar with the
concept of the "triple double", that is more than 10 of 3 separate
categories of feats within a single game of basketball. (points,
rebounds, assists, if I remember correctly)
Some k values of the series k*2^n+1 and k*2n1 will also achieve this,
but maybe they are rarer. The feats are: 10 twins, 10 Sophie Germain
primes and 10 Cunningham chains length 2 first kind, with longer
chains, say Cunningham chains of length 3, counting as two separate
chains.
In fact "Triple doubles" are proving slightly elusive. After about 4
days of trying the closest I have achieved is
k= 20943627705
Which has 9 SGs, 8 CC first kind and 10 twins, checked to n=2000
9+8+10=27 close to my best points score to date of 28
Another close one: k= 92052927781815
With 7, 9 and 9 respectively, also checked to n=2000
My search has been on payam numbers E(27) and I checked quite a lot.
Can you do better in this all round category?
Regards
Robert Smith
