A082894 a(n) is the closest number to 2^n which is divisible by n.

2, 4, 9, 16, 30, 66, 126, 256, 513, 1020, 2046, 4092, 8190, 16380, 32775, 65536, 131070, 262152, 524286, 1048580, 2097144, 4194300, 8388606, 16777224, 33554425, 67108860, 134217729, 268435468, 536870910, 1073741820, 2147483646

Offset: 1

Author

Labos Elemer, Apr 22 2003

Keywords

• nonn

Examples

			n=11: 2^11=2048 is between 2046=11.186 and 2035=11.185, closer to a(11)=2046;
Powers of two are fixed points of this map.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A082893, A082895, A082896, A082897, A082898, A082899, A082900.

Programs

Maple

A082894:=n->n*floor((floor(n/2)+2^n)/n); seq(A082894(k), k=1..100); # Wesley Ivan Hurt, Oct 29 2013

Mathematica

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

PARI

for(n=1,50, print1(n*floor( (floor(n/2)+2^n) / n ), ", ")) \\ G. C. Greubel, Aug 08 2017

Python

def A082894(n): return (m:=(1<>1))-m%n # Chai Wah Wu, Apr 23 2025

Formula

a(n) = n*floor( (floor(n/2)+2^n) / n ).