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

Offset: 1

Author

Ivan N. Ianakiev, Mar 14 2024

Keywords

• nonn
• base

Crossrefs

Cf. A353187, A371060, A371182.

Programs

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]