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A368643 Manhattan distance from the origin of triangular number point T(n) = n*(n+1)/2 in a square spiral with point 0 at the origin.

%I A368643 #31 Jan 29 2024 19:08:57
%S A368643 0,1,1,2,2,3,3,4,6,3,7,6,6,9,5,10,8,9,11,8,14,9,13,12,12,17,9,18,14,
%T A368643 15,19,12,22,15,19,20,16,25,15,24,20,21,27,16,30,21,25,28,20,35,21,30,
%U A368643 28,25,35,20,36,27,31,36,24,43,27,36,36,29,45,26,42,35,35,44,28,49,33,42,44,33,55,32,48,43,39,54,30
%N A368643 Manhattan distance from the origin of triangular number point T(n) = n*(n+1)/2 in a square spiral with point 0 at the origin.
%F A368643 a(n) = A214526(n*(n+1)/2 + 1).
%e A368643 Showing the Manhattan distance for a(4), that is, from the origin to the fourth triangular number T(4) = 10, as being 2:
%e A368643   +----15-----+-----+-----+     +
%e A368643   |                       |     |
%e A368643   |                       |     |
%e A368643   +     +-----3-----+     +    28
%e A368643   |     |           |     |     |
%e A368643   |     |           |     |     |
%e A368643   +     +     0-----1    10     +
%e A368643   |     |     ^---a(4)=2--^     |
%e A368643   |     |                 |     |
%e A368643   +     6-----+-----+-----+     +
%e A368643   |                             |
%e A368643   |                             |
%e A368643   +----21-----+-----+-----+-----+
%Y A368643 Cf. A214526, A000217.
%K A368643 nonn,easy
%O A368643 0,4
%A A368643 _Tamas Sandor Nagy_, Jan 01 2024