A221980 Number of primes of the form (x+1)^7 - x^7 with x <= 10^n.

1, 6, 24, 161, 1094, 8283, 66790

Offset

0,2

Comments

Number of primes 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 of the form (x+1)^7 - x^7 with x <= 10^n have similar characteristics to similar sequences for natural primes, cuban primes (A221794) and primes of the form (x+1)^5 - x^5 (A221849).

Links

Table of n, a(n) for n=0..6.

Mathematica

Table[Count[#[[2]]-#[[1]]&/@Partition[Range[10^n+1]^7, 2, 1], _?PrimeQ], {n, 0, 6}] (* Harvey P. Dale, Sep 17 2019 *)

Prog

(PARI) a(n) = {nb = 0; for (i = 1, 10^n, if (isprime((i+1)^7-i^7), nb++); ); nb; } \\ Michel Marcus, Sep 18 2013

Crossrefs

Sequence in context: A165638 A122829 A232688 * A359693 A225827 A375627

Adjacent sequences: A221977 A221978 A221979 * A221981 A221982 A221983

Keyword

nonn,base

Author

Vladimir Pletser, Feb 02 2013

Status

approved