A157807 Numerators 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, 2, 1, 1, 3, 4, 3, 2, 1, 1, 5, 6, 5, 4, 3, 2, 1, 1, 3, 5, 7, 8, 7, 5, 4, 2, 1, 1, 3, 7, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 5, 7, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 3, 5, 9, 11, 13, 14, 13, 11, 8, 7, 4, 2, 1, 1, 3, 5, 7, 9, 11, 13, 15, 16, 15, 14

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. A157813 (denominators), A038566.

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

Extensions

A-number in cross-reference corrected by R. J. Mathar, Sep 23 2009

a(19)-a(20) corrected and a(58)-a(82) added by Hiroaki Yamanouchi, Oct 06 2014

Name corrected by Andrey Zabolotskiy, Oct 10 2023