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A353187 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair that is not coprime. 0
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 3n-1, it seems that A003627 is a subsequence.

LINKS

Table of n, a(n) for n=1..67.

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

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Last modified August 9 17:13 EDT 2022. Contains 356026 sequences. (Running on oeis4.)