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User: William Chang

William Chang has authored 2 sequences.

A357123 Number of sets S of size A066063(n) such that {1, 2, ..., n} is a subset of S + S.

1, 1, 2, 2, 5, 5, 2, 1, 11, 8, 1, 1, 26, 16, 2, 1, 65, 39, 7, 5, 284, 183, 52, 31, 8, 3, 422, 243, 58, 31, 4, 2, 893, 475, 144, 79, 21, 11, 1, 1, 428, 233, 54, 29, 3, 2, 2034, 1180, 371, 213

Offset: 1

William Chang, Sep 12 2022

A066063(n) is the size of the smallest set S such that S+S contains {1,2,...,n}.

			For n=3 we can generate {1, 2, 3} with S = {0, 1, 2} and S = {0, 1, 3}.

William Chang, Python script

Cf. A066063.

a(31)-a(50) from Giovanni Resta, Oct 15 2022

A347208 Number of permutations of [n] that are in the same position in A030298 as they are in A098281.

Original entry on oeis.org

1, 2, 3, 3, 3, 10, 5, 4, 5, 13, 3, 6, 5

Offset: 1

William Chang, Aug 23 2021

			For n = 7 the a(7) = 5 permutations are 1234567, 1234576, 1236745, 6574231, 7654321, which are in positions 1, 2, 17, 4198, 5040 respectively in both sequences A030298 and A098281.

Cf. A030298, A098281.

perms[n_] := perms[n] = If[n == 1, {{1}}, Flatten[Table[Insert[#, n, pos], {pos, -1, -n, -1}]& /@ perms[n-1], 1]];
a[n_] := Count[Transpose@{perms[n], Permutations[Range[n]]}, {p_, p_}];
Table[a[n], {n, 1, 10}] (* Jean-François Alcover, Sep 02 2021 *)

cp's OEIS Frontend

User: William Chang

A357123 Number of sets S of size A066063(n) such that {1, 2, ..., n} is a subset of S + S.

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