A221984 Number of primes of the form (x+1)^11 - x^11 having n digits.

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, 67, 86, 75, 114, 120, 146, 191, 267, 291, 394, 470, 561, 652, 837, 1063, 1339, 1709, 2018, 2475, 3092, 3680, 4750, 5925, 7295, 9063, 11174, 14034, 17294, 21208

Offset

9,12

Comments

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).

Links

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

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

Crossrefs

Sequence in context: A103778 A099423 A221515 * A071920 A306548 A320531

Adjacent sequences: A221981 A221982 A221983 * A221985 A221986 A221987

Keyword

nonn,easy,base

Author

Vladimir Pletser, Feb 02 2013

Status

approved