A346287 - OEIS

%I #6 Jul 13 2021 09:20:04

%S 1,11,13,19,131,5851,416833471

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

%e 1 = 2^2-(2+1) = 0^2+(0+1)

%e 11 = 4^2-(4+1) = 2^3+(2+1)

%e 13 = 2^4-(2+1) = 3^2+(3+1)

%e 19 = 5^2-(5+1) = 2^4+(2+1)

%e 131 = 12^2-(12+1) = 5^3+(5+1)

%e 5851 = 77^2-(77+1) = 18^3+(18+1)

%e 416833471 = 20417^2-(20417+1) = 747^3+(747+1)

%p N:= 10^11: # for terms <= N

%p R:= {3}:

%p for k from 2 to ilog2(N-1) do

%p   R:= R union {seq(x^k+x+1,x=2..floor(N^(1/k)))}

%p od:

%p A:= {1}:

%p for k from 2 to ilog2(N+3) do

%p   for x from 2 do

%p     r:= x^k-(x+1);

%p     if r > N then break fi;

%p     if member(r,R) then A:= A union {r} fi

%p od od:

%p sort(convert(A,list));

%Y Cf. A253913.

%K nonn,more

%O 1,2

%A _J. M. Bergot_ and _Robert Israel_, Jul 12 2021