A077258 - OEIS

%I #6 Mar 30 2012 17:30:51

%S 1,4,6888,4920,187117320

%N Least number which can be represented by the difference between two successive prime powers of prime numbers (A076707) in just n ways.

%e 1 = 9-8, 4 = 8-4 & 125-121, 6888 = 332929 - 326041 = 744769 - 737881 = 2968729 - 2961841, 4920 = 44521 - 39601 = 63001 - 58081 = 380689 - 375769 = 1515361 - 1510441 and

%e 187117320 = 9725896737769 - 9725709620449 = 21883150711249 - 21882963593929 = 60786363426721 - 60786176309401 = 243145173030769 - 243144985913449 = 2188305808807561 - 2188305621690241.

%t pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^16]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^16]]]}]]]; l = Length[pp]; b = Sort[ Take[pp, -l + 1] - Take[pp, l - 1]];

%Y Cf. A053810, A075308, A076707, A077257.

%K more,nonn

%O 1,2

%A _Zak Seidov_ and _Robert G. Wilson v_, Oct 31 2002