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A284917 Lexicographically earliest infinite sequence of positive integers such that the Taxicab distance is unique to each pair of distinct points ((n, a(n)), (k, a(k)). 2
1, 1, 2, 5, 9, 16, 25, 38, 58, 72, 87, 112, 136, 169, 190, 237, 274, 344, 383, 456, 545, 572, 640, 752, 798, 891, 944, 989, 1131, 1283, 1365, 1492, 1540, 1788, 1862, 1994, 2218, 2342, 2472, 2741, 2885, 3114, 3312, 3548, 3753, 3953, 4251, 4386, 4731, 4802, 5073 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: This sequence is strictly increasing for n > 1.

LINKS

Peter Kagey and Giovanni Resta, Table of n, a(n) for n = 1..2000 (first 300 terms from Peter Kagey)

EXAMPLE

Let p_n = (n, a(n)).

For n = 4, a(4) = 5 because

d(p_1, p_4) = 3 = d(p_1, 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) = 2 = d(p_2, p_3) if a(4) = 3,

d(p_3, p_4) = 3 = 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@Abs[p - q]; good[w_] := Catch[Do[If[ MemberQ[di, dq[w, P[[i]]]], Throw@False], {i, Length@P}]; True]; di = P = {}; n = 0; While[n < 51, 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), A284916 (Euclidean distance).

Sequence in context: A282044 A138226 A175287 * A007979 A097701 A225596

Adjacent sequences:  A284914 A284915 A284916 * A284918 A284919 A284920

KEYWORD

nonn

AUTHOR

Peter Kagey, Apr 05 2017

STATUS

approved

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Last modified August 5 21:45 EDT 2020. Contains 336213 sequences. (Running on oeis4.)