OFFSET
1,4
COMMENTS
a(2*n-1) / a(2*n) is the n-th fraction in Cantor's enumeration of the positive rational numbers. - Peter Luschny, Oct 10 2023
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..9914
Georg Cantor, Ein Beitrag zur Mannigfaltigkeitslehre, Journal für die reine und angewandte Mathematik 84 (1878), 242-258, (p. 250).
N. J. A. Sloane, List of the 4957 pairs (i,j) with i+j <= 127. [Note this is not a b-file.]
EXAMPLE
The first few pairs are, seen as an irregular triangle:
[1, 1],
[1, 2], [2, 1],
[1, 3], [3, 1],
[1, 4], [2, 3], [3, 2], [4, 1],
[1, 5], [5, 1],
[1, 6], [2, 5], [3, 4], [4, 3], [5, 2], [6, 1],
[1, 7], [3, 5], [5, 3], [7, 1],
[1, 8], [2, 7], [4, 5], [5, 4], [7, 2], [8, 1],
[1, 9], [3, 7], [7, 3], [9, 1],
...
MAPLE
CantorsList := proc(upto) local C, F, n, t, count;
C := NULL; count := 0:
for n from 2 while count < upto do
F := select(t -> igcd(t, n-t) = 1, [$1..n-1]);
C := C, seq([t, n - t], t = F);
count := count + nops(F) od:
ListTools:-Flatten([C]) end:
CantorsList(40); # Peter Luschny, Oct 10 2023
MATHEMATICA
A352911row[n_]:=Select[Array[{#, n-#}&, n-1], CoprimeQ[First[#], Last[#]]&];
Array[A352911row, 10, 2] (* Generates 10 rows *) (* Paolo Xausa, Oct 10 2023 *)
PROG
(Python)
from math import gcd
from itertools import chain, count, islice
def A352911_gen(): # generator of terms
return chain.from_iterable((i, n-i) for n in count(2) for i in range(1, n) if gcd(i, n-i)==1)
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, Apr 09 2022
STATUS
approved