A160145 a(n) = the odd number 2n+1 minus the numerator of (2n+1)/(2^(2n+1)-1).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 150

Offset: 0

Author

Peter Luschny, May 03 2009

Keywords

• nonn

Comments

Explains the similarity of the sequences A009843 and A160143. (Cf. also the pair A036279 and A156769.) The first nonzero values occur at n = 10, 31, 52 and 73.

Previous name was: Odd numbers 2n+1 minus the numerators of (2n+1)/(4^(2n+1)-2^(2n+1)), (A005408 - A160144). - Altug Alkan, Apr 21 2018

Links

• Altug Alkan, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005408, A009843, A160143, A160144.

Programs

Maple

seq((2*n+1)-numer((2*n+1)/(4^(2*n+1)-2^(2*n+1))),n=0..77);
seq((2*n+1)-numer((2*n+1)/(2^(2*n+1)-1)),n=0..100); # Altug Alkan, Apr 21 2018

Mathematica

Array[# - Numerator[#/(2^# - 1)] &[2 # + 1] &, 78, 0] (* Michael De Vlieger, Apr 21 2018 *)

PARI

forstep(k=1, 1e2, 2, print1(k - numerator(k/(2^k-1)), ", ")); \\ Altug Alkan, Apr 21 2018

Formula

a(n) = A005408(n) - A160144(n).

Extensions

Name simplified by Altug Alkan, Apr 21 2018