A157813 Denominators of fractions arranged in "antidiagonal boustrophedon" ordering with equivalent fractions removed: (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, 5/2, ...).

1, 1, 2, 3, 1, 1, 2, 3, 4, 5, 1, 1, 2, 3, 4, 5, 6, 7, 5, 3, 1, 1, 2, 4, 5, 7, 8, 9, 7, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 7, 5, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 11, 9, 5, 3, 1, 1, 2, 4, 7, 8, 11, 13, 14, 15, 13, 11, 9, 7, 5, 3, 1, 1, 2, 3, 4

Offset: 1

Author

Ron R. King, Mar 07 2009

Keywords

• nonn
• frac

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A157807 (numerators), A038567.

With Cantor's ordering: A020652, A020653, A352911.

Programs

Maple

R:= NULL: count:= 0:
for m from 2 while count < 100 do
  S:= select(t -> igcd(t,m-t)=1, [$1..m-1]);
  count:= count+nops(S);
  if m::odd then R:= R, op(S) else R:= R, seq(m-t,t=S) fi;
od:
R; # Robert Israel, Oct 09 2023

Python

from math import gcd
for s in range(2, 100, 2):
  for i in range(1, s):
    if gcd(i, s - i) != 1: continue
    print(s - i)
  for i in range(s, 0, -1):
    if gcd(i, s + 1 - i) != 1: continue
    print(s + 1 - i)
# Hiroaki Yamanouchi, Oct 06 2014

Extensions

a(58)-a(83) from Hiroaki Yamanouchi, Oct 06 2014

Name corrected by Andrey Zabolotskiy, Oct 10 2023