A353187 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair that is not coprime.

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

Offset: 1

Author

Ivan N. Ianakiev, Apr 29 2022

Keywords

• nonn

Comments

Based on testing the first 1000 primes of the form 3n-1, it seems that A003627 is a subsequence.

Links

• Ivan N. Ianakiev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A047255.

Programs

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[n-2],a[n-1]];a/@Range[100]

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