cp's OEIS Frontend

A346287 Numbers that are of both forms x^k+x+1 and x^k-(x+1) with k>=2 and x>=0.

%I A346287 #6 Jul 13 2021 09:20:04
%S A346287 1,11,13,19,131,5851,416833471
%N A346287 Numbers that are of both forms x^k+x+1 and x^k-(x+1) with k>=2 and x>=0.
%e A346287 1 = 2^2-(2+1) = 0^2+(0+1)
%e A346287 11 = 4^2-(4+1) = 2^3+(2+1)
%e A346287 13 = 2^4-(2+1) = 3^2+(3+1)
%e A346287 19 = 5^2-(5+1) = 2^4+(2+1)
%e A346287 131 = 12^2-(12+1) = 5^3+(5+1)
%e A346287 5851 = 77^2-(77+1) = 18^3+(18+1)
%e A346287 416833471 = 20417^2-(20417+1) = 747^3+(747+1)
%p A346287 N:= 10^11: # for terms <= N
%p A346287 R:= {3}:
%p A346287 for k from 2 to ilog2(N-1) do
%p A346287   R:= R union {seq(x^k+x+1,x=2..floor(N^(1/k)))}
%p A346287 od:
%p A346287 A:= {1}:
%p A346287 for k from 2 to ilog2(N+3) do
%p A346287   for x from 2 do
%p A346287     r:= x^k-(x+1);
%p A346287     if r > N then break fi;
%p A346287     if member(r,R) then A:= A union {r} fi
%p A346287 od od:
%p A346287 sort(convert(A,list));
%Y A346287 Cf. A253913.
%K A346287 nonn,more
%O A346287 1,2
%A A346287 _J. M. Bergot_ and _Robert Israel_, Jul 12 2021