A221849 Number of primes of the form (x+1)^5 - x^5 with x <= 10^n.

1, 4, 25, 149, 1101, 8489, 69978, 596022, 5179467, 45811178

Offset: 0

Author

Vladimir Pletser, Jan 26 2013

Keywords

• nonn
• base

Comments

Number of primes equal to the difference of two consecutive fifth powers (x+1)^5 - x^5 = 5x(x+1)(x^2+x+1)+1 (A121616) with x <= 10^n. Values of x = A121617. Sequence of number of primes of the form (x+1)^5 - x^5 with x <= 10^n have similar characteristics to similar sequences for natural primes and cuban primes (A221794).

Programs

Mathematica

fQ[n_] := PrimeQ[(n + 1)^5 - n^5]; c = k = 0; Do[ While[k < 10^n + 1, If[ fQ@ k, c++]; k++]; Print[{n, c}], {n, 9}] (* Robert G. Wilson v, Jan 31 2013 *)

Extensions

a(7) - a(9) from Robert G. Wilson v, Jan 31 2013