A284916 Lexicographically earliest sequence of positive integers such that the same (Euclidean) distance does not occur twice between any two distinct pairs of points ((n, a(n)), (k, a(k))).

1, 1, 2, 5, 9, 14, 7, 19, 25, 2, 33, 43, 54, 67, 27, 47, 64, 78, 94, 118, 17, 129, 144, 103, 156, 174, 199, 37, 114, 199, 78, 183, 220, 168, 239, 70, 272, 302, 258, 292, 311, 350, 376, 409, 431, 458, 479, 324, 504, 550, 281, 424, 563, 527, 489, 591, 129, 636

Offset

1,3

Links

Peter Kagey and Giovanni Resta, Table of n, a(n) for n = 1..2500 (first 500 terms from Peter Kagey)

Example

Let p_n = (n, a(n)).
For n = 4, a(4) = 5 because
d(p_3, p_4) = sqrt(2) = d(p_2, p_3) if a(4) = 1,
d(p_3, p_4) = 1       = d(p_1, p_2) if a(4) = 2,
d(p_3, p_4) = sqrt(2) = d(p_2, p_3) if a(4) = 3,
d(p_3, p_4) = sqrt(5) = d(p_1, p_3) if a(4) = 4, therefore
a(4) = 5, the least value that does not create a contradiction.

Mathematica

dq[p_, q_] := Total[(p - q)^2]; good[w_] := Catch[ Do[ If[ MemberQ[di, dq[w, P[[i]]]], Throw@False], {i, Length@ P}]; True]; P = di = {}; n = 0; While[n < 58, n++; k = 1; While[! good[{n, k}], k++]; di = Join[di, dq[{n, k}, #] & /@ P]; AppendTo[P, {n, k}]]; Last /@ P (* Giovanni Resta, Apr 06 2017 *)

Crossrefs

Cf. A005282 (Chebyshev distance), A284917 (Taxicab distance).

Sequence in context: A331809 A126326 A364248 * A070986 A074793 A161767

Adjacent sequences: A284913 A284914 A284915 * A284917 A284918 A284919

Keyword

nonn,look

Author

Peter Kagey, Apr 05 2017

Status

approved