A157813 - OEIS

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

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OFFSET

1,3

LINKS

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

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

Adjacent sequences: A157810 A157811 A157812 * A157814 A157815 A157816

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