|
%I #5 Jan 11 2016 18:24:27
%S 8191,27647,62207,139967,314927,472391,1062881
%N Primes of the form 2^i*3^j - 1 with i + j = 13.
%C Note that bases 2 = prime(1), 3 = prime(2)
%C 13 = prime(2 x 3) = prime(prime(1) x prime(2))
%C Smallest term 8191 is the 5th Mersenne prime
%C It is a finite "FUN" sequence with 7 = prime(4) terms
%D Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983
%e 8191 = 2^13 - 1 = prime(1028)
%e 27647 = 2^10 x 3^3 - 1 = prime(3016) = prime(2^3 x 13 x 29)
%e 62207 = 2^8 x 3^5 - 1 = prime(6253) = prime(13^ 2 x 37)
%e 139967 = 2^6 x 3^7 - 1 = prime(13005)
%e 314927 = 2^4 x 3^9 - 1 = prime(27191), index is prime(2978)
%e 472391 = 2^3 x 3^10 - 1 = prime(39419), index is prime(4150)
%e 1062881 = 2 x 3^12 - 1 = prime(83024)
%t Select[Union[Flatten[{2^#[[1]] 3^#[[2]]-1,2^#[[2]] 3^#[[1]]-1}&/@ Table[ {n,13-n},{n,0,13}]]],PrimeQ] (* _Harvey P. Dale_, Jan 11 2016 *)
%Y Cf. A005105, A168385, A168349
%K fini,full,nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Jan 31 2010
| 