A221849 -id:A221849 - cp's OEIS frontend

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

Vladimir Pletser, Feb 02 2013

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).

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

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

A221986 Number of primes of the form (x+1)^11 - x^11 with x <= 10^n.

Original entry on oeis.org

0, 3, 9, 46, 479, 3711, 30830

Offset: 0

Vladimir Pletser, Feb 02 2013

Number of primes 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 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)^p - x^p for p = 5 (A221849) and p = 7 (A221980).

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

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A221986 Number of primes of the form (x+1)^11 - x^11 with x <= 10^n.

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