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A245811 Number of primes of the form k^(n+1) - n^k for some k > 1.

%I A245811 #26 Nov 30 2014 15:17:02
%S A245811 1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,2,0,1,0,0,0,0,0,0,0,0,0,0,
%T A245811 0,0,0,0,0,1,0,1,0,0,0,2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,
%U A245811 0,0,0,1,0,0,0,0,0,2
%N A245811 Number of primes of the form k^(n+1) - n^k for some k > 1.
%C A245811 The search radius for k is effectively limited to k<=n+1 because the subtracted term n^k has exponential growth and the added term k^(n+1) only polynomial growth as k increases. - _R. J. Mathar_, Sep 07 2014
%H A245811 Juri-Stepan Gerasimov, <a href="/A245811/b245811.txt">Table of n, a(n) for n = 1..78</a>
%p A245811 A245811 := proc(n)
%p A245811     local a,k,p ;
%p A245811     a := 0 ;
%p A245811     for k from 2 to n+1 do
%p A245811         p := k^(n+1)-n^k ;
%p A245811         if isprime(p) then
%p A245811              a := a+1 ;
%p A245811         end if;
%p A245811     end do:
%p A245811     a ;
%p A245811 end proc:
%p A245811 seq(A245811(n),n=1..120) ; # _R. J. Mathar_, Sep 07 2014
%o A245811 (PARI) a(n) = if(n==1, return(1)); my(k=2, c=0, t); while((t=k^(n+1)-n^k)>0, k++; if(isprime(t), c++)); c
%o A245811 vector(80, n, a(n)) \\ _Colin Barker_, Aug 26 2014
%Y A245811 Cf. A245809.
%K A245811 nonn
%O A245811 1,22
%A A245811 _Juri-Stepan Gerasimov_, Aug 22 2014