This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A181126 #5 Oct 23 2024 18:06:01
%S A181126 0,127,2059,2186,14197,16256,16383,61741,75938,77997,78124,201811,
%T A181126 263552,277749,279808,279935,543607,745418,807159,821356,823415,
%U A181126 823542,1273609,1817216,2019027,2080768,2094965,2097024,2097151,2685817
%N A181126 Difference of two positive 7th powers.
%C A181126 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.
%C A181126 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?
%H A181126 T. D. Noe, <a href="/A181126/b181126.txt">Table of n, a(n) for n=1..1000</a>
%t A181126 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]]]
%t A181126 Join[{0},#[[2]]-#[[1]]&/@Subsets[Range[10]^7,{2}]//Union] (* _Harvey P. Dale_, Oct 23 2024 *)
%Y A181126 Cf. A024352 (squares), A181123 (cubes), A147857 (4th powers), A181124-A181128 (5th to 9th powers)
%K A181126 nonn
%O A181126 1,2
%A A181126 _T. D. Noe_, Oct 06 2010