A082900 - OEIS

%I #11 Feb 18 2023 08:08:20

%S 0,0,1,0,-2,2,-2,0,1,-4,-2,-4,-2,-4,7,0,-2,8,-2,4,-8,-4,-2,8,-7,-4,1,

%T 12,-2,-4,-2,0,-8,-4,17,8,-2,-4,-8,-16,-2,20,-2,-16,-17,-4,-2,-16,19,

%U -24,-8,-16,-2,26,12,24,-8,-4,-2,-16,-2,-4,-8,0,-32,2,-2,-16,-8,26,-2,8,-2,-4,7,-16,-18,14,-2,-16,1,-4,-2,20,-32,-4,-8

%N a(n) = A082894(n)-A000079(n), the difference of 2^n and the number closest to it and divisible by n.

%C n=5:2^5=32 and number divisible by n=5 and closest to 32 is 30 = A082894(5), a(5)=30-32=-2 is the corresponding difference.

%H Antti Karttunen, <a href="/A082900/b082900.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n)=n*floor[(floor(n/2)+2^n)/n]-2^n

%t Table[n*Floor[(Floor[n/2]+2^n)/n]-2^n, {n, 1, 100}]

%o (PARI)

%o A082894(n) = (n*(((n\2)+2^n)\n));

%o A082900(n) = (A082894(n)-(2^n)); \\ _Antti Karttunen_, Feb 18 2023

%o (PARI) A082900(n) = { my(x=2^n); for(k=0,oo,if(!((x-k)%n),return(-k), if(!((x+k)%n),return(k)))); }; \\ _Antti Karttunen_, Feb 18 2023

%Y Cf. A082893, A082894, A082895, A082896, A082898, A082899, A082901.

%K sign,look

%O 1,5

%A _Labos Elemer_, Apr 22 2003