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%I #8 Nov 09 2021 05:53:22
%S 1,4,2,3,8,6,9,7,15,10,16,11,24,5,27,13,22,20,14,31,25,12,26,33,40,21,
%T 44,19,55,23,18,36,32,35,48,51,34,46,17,42,47,30,37,43,63,82,28,45,61,
%U 52,62,38,50,78,57,79,41,65,29,70,39,59,97,66,98,67,80,68,49,101,69,119,53,124,71,60
%N a(0) = 1; for n>0, a(n) is the smallest positive integer that has not previously occurred such that |n - a(n-1)| + a(n) is a square.
%H Scott R. Shannon, <a href="/A349119/a349119.png">Image of the first 1000000 terms</a>.
%e a(1) = 4 as |1 - a(0)| = |1 - 1| = 0, and 0 + 4 = 4 = 2^2 is the next smallest square. Note a(1) cannot be 1 as a(0) = 1.
%e a(4) = 8 as |4 - a(3)| = |4 - 3| = 1, and 1 + 8 = 9 = 3^2 is the next smallest square. Note a(4) cannot be 3 as a(3) = 3.
%e a(8) = 15 as |8 - a(7)| = |8 - 7| = 1, and 1 + 15 = 16 = 4^2 is the next smallest square. Note a(8) cannot be 3 or 8 as these have previously occurred.
%Y Cf. A349182, A000290, A347595, A347594, A009000, A347754.
%K nonn,look
%O 0,2
%A _Scott R. Shannon_, Nov 08 2021
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