A221983 Number of primes of the form (x+1)^11 - x^11 less than 10^n.

1, 2, 3, 3, 4, 4, 4, 4, 5, 6, 6, 8, 9, 9, 9, 12, 15, 18, 24, 30, 35, 41, 46, 66, 83, 104, 133, 166, 195, 247, 314, 400, 475, 589, 709, 855, 1046, 1313, 1604, 1998, 2468, 3029, 3681, 4518, 5581, 6920, 8629, 10647, 13122, 16214, 19894, 24644, 30569, 37864, 46927

Offset: 9

Author

Vladimir Pletser, Feb 02 2013

Keywords

• nonn

Comments

Number of primes less than 10^n 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 less than 10^n and of the form (x+1)^11 - x^11 have similar characteristics to similar sequences for natural primes (A006880), cuban primes (A113478) and primes of the form (x+1)^p - x^p for p = 5 (A221846) and p = 7 (A221977).

Links

• Vladimir Pletser, Table of n, a(n) for n = 9..86

Programs

Mathematica

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]]++]]; Accumulate[t] (* T. D. Noe, Feb 04 2013 *)