A161602 - OEIS

%I #29 Jan 20 2023 01:35:07

%S 2,4,6,8,10,12,13,14,16,18,20,22,24,25,26,28,29,30,32,34,36,38,40,41,

%T 42,44,46,48,49,50,52,53,54,56,57,58,59,60,61,62,64,66,68,70,72,74,76,

%U 78,80,81,82,84,86,88,89,90,92,94,96,97,98,100,101,102,104,105,106,108,109

%N Positive integers k that are greater than the value of the reversal of k's binary representation.

%C By "reversal" of k's binary representation, it is meant: write k in binary, reverse the order of its digits, and read the result as a binary value.

%C This sequence contains all the positive even integers.

%H Jonathan Frech, <a href="/A161602/b161602.txt">Table of n, a(n) for n = 1..10000</a>

%e 29 in binary is 11101. Its digital reversal is 10111, which is 23 in decimal. Since 29 > 23, 29 is in this sequence.

%t Select[Range[109], # > IntegerReverse[#, 2] &] (* _Michael De Vlieger_, Apr 07 2021 *)

%o (PARI) isok(k) = k > fromdigits(Vecrev(binary(k)), 2); \\ _Michel Marcus_, Apr 06 2021

%o (Python)

%o from itertools import count, islice

%o def A161602_gen(startvalue=1): # generator of terms >= startvalue

%o     return filter(lambda n:n>int(bin(n)[-1:1:-1],2),count(max(startvalue,1)))

%o A161602_list = list(islice(A161602_gen(),20)) # _Chai Wah Wu_, Jan 19 2023

%Y Cf. A030101, A006995, A161601, A161603 (odd terms).

%Y Cf. A071590 (using decimal reversal).

%K base,nonn

%O 1,1

%A _Leroy Quet_, Jun 14 2009

%E More terms from _Max Alekseyev_, Sep 11 2009