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

1,2

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

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]

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

Cf. A047255.

Sequence in context: A082851 A091207 A284525 * A099247 A192583 A240064

Adjacent sequences: A353184 A353185 A353186 * A353188 A353189 A353190

Keyword

nonn

Author

Ivan N. Ianakiev, Apr 29 2022

Status

approved