A371060 -id:A371060 - cp's OEIS frontend

A371182 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive digits contains only one pair that is not coprime.

1, 2, 4, 5, 6, 8, 10, 21, 22, 32, 33, 42, 52, 54, 55, 62, 72, 74, 76, 77, 82, 92, 93, 100, 102, 103, 104, 105, 106, 107, 108, 109, 130, 133, 136, 139, 160, 162, 163, 164, 166, 168, 169, 190, 193, 196, 199, 221, 223, 225, 227, 229, 232, 233, 234, 238, 239, 241, 243, 245

Offset: 1

Ivan N. Ianakiev, Mar 14 2024

Cf. A353187, A371060, A371183.

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[4]=5;a[5]=6;a[6]=8;a[7]=10;
a[n_]:=a[n]=Module[{k=a[n-1]+1,digits},
While[digits=Join[Take[IntegerDigits[a[n-1]],-2],IntegerDigits[k]];
Union[ pairwiseQ@@@Table[{digits[[i]],digits[[i+1]],digits[[i+2]]},
{i,1,Length[digits]-2}]]!={True},k++];k]; a/@Range[60]

A371183 Lexicographically earliest sequence of distinct terms in which every triple of consecutive digits contains only one pair that is not coprime.

Original entry on oeis.org

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

Ivan N. Ianakiev, Mar 14 2024

Cf. A353187, A371060, A371182.

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]

cp's OEIS Frontend

A371182 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive digits contains only one pair that is not coprime.

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