A352450 - OEIS

%I #11 Mar 20 2022 18:29:59

%S 0,0,0,2,0,0,4,6,0,8,8,10,0,8,12,14,0,0,0,2,16,16,20,22,0,8,8,10,16,

%T 24,28,30,0,32,0,34,32,32,36,38,0,40,8,42,32,40,44,46,0,32,0,34,48,48,

%U 52,54,0,40,8,42,48,56,60,62,0,0,64,66,64,64,68,70,0

%N 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n > 0 (where AND denotes the bitwise AND operator).

%C The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.

%H Rémy Sigrist, <a href="/A352450/b352450.txt">Table of n, a(n) for n = 0..8192</a>

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

%F a(n) <= n with equality iff n = 0.

%e For n = 42:

%e - 42 = 2^5 + 2^3 + 2^1,

%e - 42 AND 5 = 0,

%e - 42 AND 3 = 2 > 0,

%e - 42 AND 1 = 0,

%e - so a(42) = 2^3 = 8.

%o (PARI) a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m,2); if (bitand(n, k), v+=2^k)); v }

%Y See A352449, A352451, A352452, A352458 for similar sequences.

%K nonn,base

%O 0,4

%A _Rémy Sigrist_, Mar 16 2022