A342123 - OEIS

%I #18 Mar 01 2021 11:53:54

%S 0,0,0,0,0,0,0,0,0,0,11,0,2,0,0,0,0,0,19,0,0,9,23,0,6,4,0,0,6,0,0,0,0,

%T 0,35,0,37,13,39,0,4,0,43,5,0,17,47,0,14,12,0,8,10,0,55,0,18,12,4,0,

%U 14,0,0,0,0,0,67,0,69,21,71,0,0,33,75,1,77,21

%N a(n) is the remainder when n is divided by its binary reverse.

%C The binary reverse of a number is given by A030101.

%C This sequence is the analog of A071955 for the binary base.

%H Rémy Sigrist, <a href="/A342123/b342123.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = n mod A030101(n).

%F a(n) <= n with equality iff n belongs to A161601.

%F a(n) = 0 iff n belongs to A057890.

%e For n = 43,

%e - the binary reverse of 43 ("101011" in binary) is 53 ("110101" in binary),

%e - so a(43) = 43 mod 53 = 43.

%o (PARI) a(n, base=2) = { my (r=fromdigits(Vecrev(digits(n, base)), base)); n%r }

%o (Python)

%o def A342123(n): return n % int(bin(n)[:1:-1],2) if n > 0 else 0 # _Chai Wah Wu_, Mar 01 2021

%Y Cf. A030101, A057890, A071955, A161601, A342121, A342122.

%K nonn,base,look,easy

%O 1,11

%A _Rémy Sigrist_, Feb 28 2021