|
%I #5 Feb 04 2013 18:23:36
%S 1,1,1,0,1,0,0,0,1,1,0,2,1,0,0,3,3,3,6,6,5,6,5,20,17,21,29,33,29,52,
%T 67,86,75,114,120,146,191,267,291,394,470,561,652,837,1063,1339,1709,
%U 2018,2475,3092,3680,4750,5925,7295,9063,11174,14034,17294,21208
%N Number of primes of the form (x+1)^11 - x^11 having n digits.
%C Number of primes having n digits and equal to the difference of two consecutive eleventh powers (x+1)^11 - x^11 = 11x(x+1)(x^2+x+1)[ x(x+1)(x^2+x+1)(x^2+x+3)+1] +1 (A189055). Values of x = A211184. Sequence of number of primes having n digits and of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A006879), cuban primes (A221792) and primes of the form (x+1)^p - x^p for p = 5 (A221847) and p = 7 (A221978).
%H Vladimir Pletser, <a href="/A221984/b221984.txt">Table of n, a(n) for n = 9..86</a>
%t nn = 40; t = Table[0, {nn}]; n = 0; While[n++; p = (n + 1)^11 - n^11; p < 10^nn, If[PrimeQ[p], m = Ceiling[Log[10, p]]; t[[m]]++]]; t (* _T. D. Noe_, Feb 04 2013 *)
%K nonn,easy,base
%O 9,12
%A _Vladimir Pletser_, Feb 02 2013
|
