A143114 a(n) = the smallest positive integer that is coprime to n and has the same number of (nonleading) 0's in its binary representation as n has in binary.

1, 5, 1, 9, 2, 5, 1, 17, 4, 9, 2, 19, 2, 5, 1, 33, 8, 17, 4, 17, 4, 9, 2, 17, 4, 9, 2, 9, 2, 11, 1, 65, 16, 33, 8, 67, 8, 17, 4, 33, 8, 17, 4, 17, 4, 9, 2, 67, 8, 17, 4, 17, 4, 19, 2, 17, 4, 9, 2, 19, 2, 5, 1, 129, 32, 65, 16, 65, 16, 33, 8, 65, 16, 33, 8, 33, 8, 17, 4, 131, 16, 33, 8, 67

Offset

1,2

Links

Owen Whitby, Table of n, a(n) for n=1..200

Example

For n = 20: 20 in binary is 10100, which has three 0's. The positive integers that each have three 0's in their binary representations are 8,17,18,20, etc. The smallest of these that is coprime to 20 is 17. So a(20) = 17.

Mathematica

spi[n_]:=Module[{z=DigitCount[n, 2, 0], k=1}, While[DigitCount[k, 2, 0]!=z || !CoprimeQ[ k, n], k++]; k]; Array[spi, 90] (* Harvey P. Dale, Apr 19 2016 *)

Crossrefs

Cf. A143113.

Sequence in context: A147319 A147326 A336048 * A103133 A098318 A360750

Adjacent sequences: A143111 A143112 A143113 * A143115 A143116 A143117

Keyword

base,nonn

Author

Leroy Quet, Jul 25 2008

Extensions

a(21) to a(200) from Owen Whitby, Oct 22 20=

Status

approved