A366192 Pairs (i, j) of noncoprime positive integers sorted first by i + j then by i.

2, 2, 2, 4, 3, 3, 4, 2, 2, 6, 4, 4, 6, 2, 3, 6, 6, 3, 2, 8, 4, 6, 5, 5, 6, 4, 8, 2, 2, 10, 3, 9, 4, 8, 6, 6, 8, 4, 9, 3, 10, 2, 2, 12, 4, 10, 6, 8, 7, 7, 8, 6, 10, 4, 12, 2, 3, 12, 5, 10, 6, 9, 9, 6, 10, 5, 12, 3, 2, 14, 4, 12, 6, 10, 8, 8, 10, 6, 12, 4, 14, 2

Offset

1,1

Comments

The rows of A290600 interleaved term by term with the reversed rows of A290600. - Peter Munn, Jan 28 2024

Links

Paolo Xausa, Table of n, a(n) for n = 1..9886

Example

The first few pairs are, seen as an irregular triangle (where rows with a prime index are empty (and are therefore missing)):
  [2,  2],
  [2,  4], [3,  3], [4, 2],
  [2,  6], [4,  4], [6, 2],
  [3,  6], [6,  3],
  [2,  8], [4,  6], [5, 5], [6, 4], [ 8, 2],
  [2, 10], [3,  9], [4, 8], [6, 6], [ 8, 4], [ 9, 3], [10, 2],
  [2, 12], [4, 10], [6, 8], [7, 7], [ 8, 6], [10, 4], [12, 2],
  [3, 12], [5, 10], [6, 9], [9, 6], [10, 5], [12, 3],
  ...
There are A016035(n) pairs in row n.

Maple

aList := proc(upto) local F, P, n, t, count;
P := NULL; count := 0:
for n from 2 while count < upto do
    F := select(t -> igcd(t, n - t) <> 1, [$1..n-1]);
    P := P, seq([t, n - t], t = F);
    count := count + nops([F]) od:
ListTools:-Flatten([P]) end:
aList(16);

Mathematica

A366192row[n_]:=Select[Array[{#, n-#}&, n-1], !CoprimeQ[First[#], Last[#]]&];
Array[A366192row, 20, 2] (* Paolo Xausa, Nov 28 2023 *)

Prog

(Python)
from math import gcd
from itertools import chain, count, islice
def A366192_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)
A366192_list = list(islice(A366192_gen(), 30)) # Chai Wah Wu, Oct 10 2023

Crossrefs

Cf. A016035, A290600 (first bisection), A352911 (complement).

Sequence in context: A050493 A331851 A335607 * A347628 A338796 A085454

Adjacent sequences: A366189 A366190 A366191 * A366193 A366194 A366195

Keyword

nonn,look,tabf,easy

Author

Peter Luschny, Oct 10 2023

Status

approved