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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, ...).
5
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
1,3
LINKS
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
PROG
(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
CROSSREFS
Cf. A157807 (numerators), A038567.
With Cantor's ordering: A020652, A020653, A352911.
Sequence in context: A352924 A327192 A351651 * A111879 A193280 A114732
KEYWORD
nonn,frac
AUTHOR
Ron R. King, Mar 07 2009
EXTENSIONS
a(58)-a(83) from Hiroaki Yamanouchi, Oct 06 2014
Name corrected by Andrey Zabolotskiy, Oct 10 2023
STATUS
approved