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a(n) = prime(n)^prime(n+1) - prime(n+1)^prime(n).
2

%I #17 Sep 08 2022 08:45:35

%S -1,118,61318,1957839572,32730551749894,8640511341348431996,

%T 233592048827366522661214,257755012474380136537664158772,

%U 3091054326372819773383775097721670599074,2141662167055484666186673758527328459608763158

%N a(n) = prime(n)^prime(n+1) - prime(n+1)^prime(n).

%C a(n) > 0 for n>=2. - _Robert Israel_, Nov 02 2014

%C a(n) = A053089(n) - A078422(n). - _Michel Marcus_, Oct 10 2016

%H Robert Israel, <a href="/A140893/b140893.txt">Table of n, a(n) for n = 1..70</a>

%e n=1: a(1) = prime(1)^prime(1+1) - prime(1+1)^prime(1) = 2^3 - 3^2 = 8 - 9 = -1.

%e n=3: a(3) = prime(3)^prime(4) - prime(4)^prime(3) = 5^7 - 7^5 = 78125 - 16807 = 61318.

%p seq(ithprime(i)^ithprime(i+1)-ithprime(i+1)^ithprime(i), i=1..20); # _Robert Israel_, Nov 02 2014

%t Array[Prime[ # ]^Prime[ #+1]-Prime[ #+1]^Prime[ # ]&,16] (* _Vladimir Joseph Stephan Orlovsky_, Oct 11 2009 *)

%o (Magma) [NthPrime(n)^NthPrime(n+1)-NthPrime(n+1)^NthPrime(n): n in [1..10]]; // _Vincenzo Librandi_, Nov 02 2014

%Y Cf. A000040, A007965, A143776.

%K sign

%O 1,2

%A _Juri-Stepan Gerasimov_, Jul 07 2008

%E Corrected and extended by _Vladimir Joseph Stephan Orlovsky_, Oct 11 2009

%E a(10) from _Vincenzo Librandi_, Nov 02 2014