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

0, 0, 1, 1, 2, 3, 6, 7, 8, 10, 14, 18, 25, 34, 46, 60, 89, 120, 165, 227, 298, 415, 590, 821, 1152, 1606, 2240, 3188, 4438, 6208, 8714, 12280, 17368, 24560, 34821, 49413, 70581, 100856, 143955, 205291, 293061, 419256, 600213, 858870, 1230523, 1764914, 2532078

Offset: 1

Author

Vladimir Pletser, Feb 02 2013

Keywords

• nonn
• base

Comments

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).

Links

• Vladimir Pletser, Table of n, a(n) for n = 1..50

Programs

Mathematica

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 *)