A309497 = {27, -18, 1, 4, 23, 26, 13, 32, 19, 22, 41, 44, 31, 18, 37,
   24, 27, 46, 33, 36, 23, -6, -3, 16, 19, 38, 41, 12, -1, 2, -11, 8,
   11, -2, 17, 4, -9, -6, 13, 16, 3, 22, 9, 12, 31, 34, 53, 8};
A286941 = {1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
   67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131,
    137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187,
   191, 193, 197, 199, 209};
x = 35;

(*
A309497={11,2,1,8,7,14,13,4};
A286941={1,7,11,13,17,19,23,29};
x=15;
*)

(*x is denominator of A038110/A060753 ie denominator of: 4/15, 8/35, \
16/77*)

b = {};
For[i = 1, i <= Length[A309497], i++,
 AppendTo[b, x*i]
 ]
b

z = Mod[b,
  A286941] (*matches A309497 for positive values in A309497*)
Quotient[b, A286941]

Intersection[Mod[b, A286941], A309497]
Position[Mod[b, A286941], A309497]

matches = {};
notMatches = {};
matchPositions = {};
notMatchesPositions = {};
notMatchesA309497 = {};
For[i = 1, i <= Length[A309497], i++,
 If[z[[i]] == A309497[[i]],
  AppendTo[matches, z[[i]]];
  AppendTo[matchPositions, i],
  AppendTo[notMatches, z[[i]]];
  AppendTo[notMatchesA309497, A309497[[i]]];
  AppendTo[notMatchesPositions, i]
  ]
 ]
Length[A309497]
Length[matches]
matches
Length[notMatches]
notMatches
Length[notMatchesA309497]
notMatchesA309497
matchPositions
notMatchesPositions

(*
test for deleted sequence that is similar to A309497 to see if it has \
the same pattern of matches etc
https://github.com/jmorken/math/tree/master/20200814%20A324591%\
20sequence%20recycled%20related%20to%20A309497
*)