cp's OEIS Frontend

A354111 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that for any 2 X 2 square of numbers both the sum of those numbers and the sum of the digits of those numbers add up to a square. Start with a(0) = 0.

%I A354111 #14 May 23 2022 17:46:32
%S A354111 0,1,2,6,3,7,4,5,19,8,141,25,9,133,28,132,10,24,135,23,11,131,29,91,
%T A354111 26,12,98,378,32,78,13,44,39,124,157,230,14,275,220,105,178,229,15,69,
%U A354111 365,51,54,153,385,16,163,303,62,104,227,123,17,43,476,66,212,83,106,134,18,30,210,195,56
%N A354111 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that for any 2 X 2 square of numbers both the sum of those numbers and the sum of the digits of those numbers add up to a square. Start with a(0) = 0.
%e A354111 The board is numbered with the square spiral:
%e A354111 .
%e A354111   10--132--28--133--9   .
%e A354111    |                |   .
%e A354111   24   3---6---2   25   32
%e A354111    |   |       |    |   |
%e A354111   135  7   0---1   141 378
%e A354111    |   |            |   |
%e A354111   23   4---5---19---8   98
%e A354111    |                    |
%e A354111   11--131--29--91--26---12
%e A354111 .
%e A354111 .
%e A354111 0 + 1 + 2 + 6 = 9 = 3^2;
%e A354111 0 + 6 + 3 + 7 = 16 = 4^2;
%e A354111 0 + 5 + 19 + 1 = 25 = 5^2, and 0 + 5 + 1 + 9 + 1 = 16 = 4^2;
%e A354111 0 + 7 + 4 + 5 = 16 = 4^2;
%e A354111 1 + 141 + 25 + 2 = 169 = 13^2, and 1 + 1 + 4 + 1 + 2 + 5 + 2 = 16 = 4^2;
%e A354111 141 + 378 + 32 + 25 = 576 = 24^2, and 1 + 4 + 1 + 3 + 7 + 8 + 3 + 2 + 2 + 5 = 36 = 6^2;
%Y A354111 Cf A337115, A347333, A344660, A344659.
%K A354111 nonn,base
%O A354111 0,3
%A A354111 _Scott R. Shannon_ and _Eric Angelini_, May 17 2022