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A361742 Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, the m X m square with lower left corner at (m, a(m)) and the n X n square with lower left corner at (n, a(n)) do not overlap (they can however touch).

%I A361742 #14 Apr 10 2023 06:50:24
%S A361742 0,0,2,5,9,14,20,0,27,36,46,8,57,70,84,99,115,132,150,20,169,190,212,
%T A361742 235,259,40,284,311,339,66,368,399,431,96,464,499,535,130,572,0,611,
%U A361742 652,694,168,737,782,828,875,923,212,972,1023,1075,1128,1182,262,1237
%N A361742 Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, the m X m square with lower left corner at (m, a(m)) and the n X n square with lower left corner at (n, a(n)) do not overlap (they can however touch).
%C A361742 This sequence is a variant of A361697.
%H A361742 Neal Gersh Tolunsky, <a href="/A361742/b361742.txt">Table of n, a(n) for n = 1..10000</a>
%H A361742 Rémy Sigrist, <a href="/A361742/a361742.txt">C++ program</a>
%H A361742 Rémy Sigrist, <a href="/A361742/a361742_1.txt">C++ program (faster)</a>
%H A361742 Rémy Sigrist, <a href="/A361742/a361742.gp.txt">PARI program</a>
%F A361742 a(n) < A000217(n).
%e A361742 The first 8 boxes are arranged as follows (note that the X and Y axes have been swapped for practical reasons):
%e A361742        88888888
%e A361742        88888888
%e A361742      n 88888888            7777777
%e A361742        88888888            7777777
%e A361742      ^ 88888888      6666667777777
%e A361742      | 88888888      6666667777777
%e A361742      | 88888888 555556666667777777
%e A361742    8 | 88888888 555556666667777777
%e A361742    7 |      4444555556666667777777
%e A361742    6 |      444455555666666
%e A361742    5 |   333444455555
%e A361742    4 |   3334444
%e A361742    3 | 22333
%e A361742    2 | 22
%e A361742    1 | 1
%e A361742        -------------------------------> a(n)
%e A361742                  11111111112222222222
%e A361742        012345678901234567890123456789
%e A361742 .
%e A361742 so a(1) = a(2) = a(8) = 0,
%e A361742    a(3) = 2,
%e A361742    a(4) = 5,
%e A361742    a(5) = 9,
%e A361742    a(6) = 14,
%e A361742    a(7) = 20.
%o A361742 (C++) See Links section.
%o A361742 (PARI) See Links section.
%Y A361742 Cf. A000217, A289523, A361697.
%K A361742 nonn
%O A361742 1,3
%A A361742 _Rémy Sigrist_, Mar 22 2023