A152810 - OEIS

A152810

Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k's that are even, o(n) the number that are odd; sequence gives odd n such that e(n) > o(n) and e(n)-o(n) == 1 or 2 (mod 6).

%I #8 Sep 12 2019 10:50:16

%S 1,5,7,13,17,19,23,25,29,31,37,49,53,55,61,65,67,71,73,77,79,83,89,91,

%T 95,97,101,103,109,113,115,119,121,125,127,133,145,149,151,157,181,

%U 193,197,199,205,209,211,215,217,221,223,229,241,245,247,253,257,259

%N Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k's that are even, o(n) the number that are odd; sequence gives odd n such that e(n) > o(n) and e(n)-o(n) == 1 or 2 (mod 6).

%C Primes in the sequence are not in A065049.

%H Amiram Eldar, <a href="/A152810/b152810.txt">Table of n, a(n) for n = 1..10000</a>

%t aQ[n_] := Module[{d = Reverse[IntegerDigits[n, 2]]}, e = Total@d[[1 ;; -1 ;; 2]]; o = Total@d[[2 ;; -1 ;; 2]]; e > o && MemberQ[{1, 2}, Mod[e - o, 6]]]; Select[Range[1, 260, 2], aQ] (* _Amiram Eldar_, Sep 12 2019 *)

%Y Cf. A065049, A139370, A152754.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Dec 13 2008

%E More terms from _Amiram Eldar_, Sep 12 2019