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URL: https://oeis.org/A284916

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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))).
3
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 A388975 A074793
KEYWORD
nonn,look
AUTHOR
Peter Kagey, Apr 05 2017
STATUS
approved