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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)). 2

%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

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)