%I
%S 1,1,2,5,9,14,7,19,25,2,33,43,54,67,27,47,64,78,94,118,17,129,144,103,
%T 156,174,199,37,114,199,78,183,220,168,239,70,272,302,258,292,311,350,
%U 376,409,431,458,479,324,504,550,281,424,563,527,489,591,129,636
%N 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)).
%H Peter Kagey and Giovanni Resta, <a href="/A284916/b284916.txt">Table of n, a(n) for n = 1..2500</a> (first 500 terms from Peter Kagey)
%e Let p_n = (n, a(n)).
%e For n = 4, a(4) = 5 because
%e d(p_3, p_4) = sqrt(2) = d(p_2, p_3) if a(4) = 1,
%e d(p_3, p_4) = 1 = d(p_1, p_2) if a(4) = 2,
%e d(p_3, p_4) = sqrt(2) = d(p_2, p_3) if a(4) = 3,
%e d(p_3, p_4) = sqrt(5) = d(p_1, p_3) if a(4) = 4, therefore
%e a(4) = 5, the least value that does not create a contradiction.
%t 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 *)
%Y Cf. A005282 (Chebyshev distance), A284917 (Taxicab distance).
%K nonn,look
%O 1,3
%A _Peter Kagey_, Apr 05 2017
