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A221977 Number of primes of the form (x+1)^7 - x^7 less than 10^n. 3

%I #12 Sep 18 2013 02:58:46

%S 0,0,1,1,2,3,6,7,8,10,14,18,25,34,46,60,89,120,165,227,298,415,590,

%T 821,1152,1606,2240,3188,4438,6208,8714,12280,17368,24560,34821,49413,

%U 70581,100856,143955,205291,293061,419256,600213,858870,1230523,1764914,2532078

%N Number of primes of the form (x+1)^7 - x^7 less than 10^n.

%C Number of primes less than 10^n and 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 less than 10^n and of the form (x+1)^7 - x^7 have similar characteristics to similar sequences for natural primes (A006880), cuban primes (A113478) and primes of the form (x+1)^5 - x^5 (A221846).

%H Vladimir Pletser, <a href="/A221977/b221977.txt">Table of n, a(n) for n = 1..50</a>

%t nn = 20; t = Table[0, {nn}]; n = 0; While[n++; p = (n + 1)^7 - n^7; p < 10^nn,If[PrimeQ[p], m = Ceiling[Log[10, p]]; t[[m]]++]]; Accumulate[t] (* _T. D. Noe_, Feb 04 2013 *)

%K nonn,base

%O 1,5

%A _Vladimir Pletser_, Feb 02 2013

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)