A221980 - OEIS

%I #11 Sep 17 2019 15:26:35

%S 1,6,24,161,1094,8283,66790

%N Number of primes of the form (x+1)^7 - x^7 with x <= 10^n.

%C Number of primes equal to the difference of two consecutive seventh powers (x+1)^7 - x^7 = 7x(x+1)(x^2+x+1)^2+1  (A121618). Values of x = A121619 - 1.  Sequence of number of primes of the form (x+1)^7 - x^7 with x <= 10^n have similar characteristics to similar sequences for natural primes, cuban primes (A221794) and primes of the form (x+1)^5 - x^5 (A221849).

%t Table[Count[#[[2]]-#[[1]]&/@Partition[Range[10^n+1]^7,2,1],_?PrimeQ],{n,0,6}] (* _Harvey P. Dale_, Sep 17 2019 *)

%o (PARI) a(n) = {nb = 0; for (i = 1, 10^n, if (isprime((i+1)^7-i^7), nb++);); nb;} \\ _Michel Marcus_, Sep 18 2013

%K nonn,base

%O 0,2

%A _Vladimir Pletser_, Feb 02 2013