A181126 Difference of two positive 7th powers.

0, 127, 2059, 2186, 14197, 16256, 16383, 61741, 75938, 77997, 78124, 201811, 263552, 277749, 279808, 279935, 543607, 745418, 807159, 821356, 823415, 823542, 1273609, 1817216, 2019027, 2080768, 2094965, 2097024, 2097151, 2685817

Offset

1,2

Comments

Because x^7-y^7 = (x-y)(x^6+x^5*y+x^4*y^2+x^3*y^3+x^2*y^4+x*y^5+y^6), the difference of two 7th powers is a prime number only if x=y+1, in which case all the primes are in A121618.

The number 67675234241018881 = 127^8 is the first of an infinite number of squares of the form (b^(7k)-1)^8 in this sequence. Are any other squares possible?

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Mathematica

nn=10^12; p=7; Union[Reap[Do[n=i^p-j^p; If[n<=nn, Sow[n]], {i, Ceiling[(nn/p)^(1/(p-1))]}, {j, i}]][[2, 1]]]

Crossrefs

Cf. A024352 (squares), A181123 (cubes), A147857 (4th powers), A181124-A181128 (5th to 9th powers)

Sequence in context: A258013 A258005 A258015 * A228263 A228222 A022523

Adjacent sequences: A181123 A181124 A181125 * A181127 A181128 A181129

Keyword

nonn

Author

T. D. Noe, Oct 06 2010

Status

approved