A371183 - OEIS

A371183

Lexicographically earliest sequence of distinct terms in which every triple of consecutive digits contains only one pair that is not coprime.

1, 2, 4, 3, 8, 9, 22, 5, 6, 21, 20, 10, 7, 17, 71, 70, 12, 23, 24, 14, 25, 26, 13, 31, 30, 15, 51, 50, 16, 27, 28, 18, 29, 32, 33, 19, 34, 38, 39, 42, 52, 41, 40, 100, 102, 103, 104, 105, 106, 107, 108, 109, 130, 120, 122, 54, 43, 35, 36, 53, 37, 62, 55, 44, 56, 45, 46, 58, 47, 48

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..70.

MATHEMATICA

pairwiseQ[a_, b_, c_]:=Sort[{CoprimeQ[a, b], CoprimeQ[b, c], CoprimeQ[a, c]}]=={False, True, True}; a[1]=1; a[2]=2; a[3]=4;

a[n_]:=a[n]=Module[{k=1, digits, tab=Table[a[i], {i, 1, n-1}]},

While[digits=Join[Take[Flatten[IntegerDigits[Take[tab, -3]]], -3], IntegerDigits[k]];

MemberQ[tab, k]||Union[pairwiseQ@@@

Table[{digits[[i]], digits[[i+1]], digits[[i+2]]},

{i, 1, Length[digits]-2}]]!={True}, k++]; k]; a/@Range[70]