A265852 - OEIS

%I #8 Dec 16 2015 18:50:19

%S 0,1,3,5,7,9,15,17,31,33,35,39,41,63,65,67,79,81,103,105,127,129,131,

%T 133,135,143,145,159,161,163,169,231,255,257,259,261,265,287,289,319,

%U 321,323,359,391,399,401,419,425,511,513,515,517,519,527,543,545

%N n such that A261807(n) = n^3 - n.

%C n such that the base-2 representation of n^3 has a 1 whenever the representation of n has a 1.

%C All terms after the first are odd.

%C Contains A083318 and A000225.

%H Robert Israel, <a href="/A265852/b265852.txt">Table of n, a(n) for n = 1..10000</a>

%e 5 is in the sequence because A261807(5) = 120 = 5^3 - 5.  The base-2 representations of 5 and 5^3 are 101 and 1111101, and every 1 in 101 corresponds to a 1 in 1111101.

%p select(t -> Bits[Xor](t,t^3) = t^3 - t, [$0..10000]);

%o (PARI) for(n=0, 1e3, if(bitxor(n, n^3) == n^3-n, print1(n, ", "))) \\ _Altug Alkan_, Dec 16 2015

%Y Cf. A261807.

%K nonn,base

%O 1,3

%A _Robert Israel_, Dec 16 2015