

A353187


Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair that is not coprime.


4



1, 2, 4, 5, 6, 8, 11, 12, 14, 17, 18, 20, 23, 24, 26, 29, 30, 32, 37, 38, 40, 41, 42, 44, 47, 48, 50, 53, 54, 56, 59, 60, 62, 67, 68, 70, 71, 72, 74, 77, 78, 80, 83, 84, 86, 89, 90, 92, 97, 98, 100, 101, 102, 104, 107, 108, 110, 113, 114, 116, 119, 120, 122, 127, 128, 130, 131
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Based on testing the first 1000 primes of the form 3n1, it seems that A003627 is a subsequence.


LINKS



MATHEMATICA

next[n_, m_]:=Piecewise[{
{(k=m+1; While[!CoprimeQ[k, n]!CoprimeQ[k, m], k++]; k), AllTrue[{n, m}, EvenQ]},
{m+2, OddQ[n]&&EvenQ[m]}, {m+1, EvenQ[n]&&OddQ[m]}}];
a[1]=1; a[2]=2; a[n_]:=a[n]=next[a[n2], a[n1]]; a/@Range[100]


PROG

(PARI) { for (v=1, 122, if (v<=2  ((gcd(pp, p)==1) + (gcd(p, v)==1) + (gcd(v, pp)==1))==2, print1 (v", "); [pp, p]=[p, v])) } \\ Rémy Sigrist, May 01 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



