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.

0, 1, 2, 6, 3, 7, 4, 5, 19, 8, 141, 25, 9, 133, 28, 132, 10, 24, 135, 23, 11, 131, 29, 91, 26, 12, 98, 378, 32, 78, 13, 44, 39, 124, 157, 230, 14, 275, 220, 105, 178, 229, 15, 69, 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

Offset

0,3

Links

Table of n, a(n) for n=0..68.

Example

The board is numbered with the square spiral:
.
  10--132--28--133--9   .
   |                |   .
  24   3---6---2   25   32
   |   |       |    |   |
  135  7   0---1   141 378
   |   |            |   |
  23   4---5---19---8   98
   |                    |
  11--131--29--91--26---12
.
.
0 + 1 + 2 + 6 = 9 = 3^2;
0 + 6 + 3 + 7 = 16 = 4^2;
0 + 5 + 19 + 1 = 25 = 5^2, and 0 + 5 + 1 + 9 + 1 = 16 = 4^2;
0 + 7 + 4 + 5 = 16 = 4^2;
1 + 141 + 25 + 2 = 169 = 13^2, and 1 + 1 + 4 + 1 + 2 + 5 + 2 = 16 = 4^2;
141 + 378 + 32 + 25 = 576 = 24^2, and 1 + 4 + 1 + 3 + 7 + 8 + 3 + 2 + 2 + 5 = 36 = 6^2;

Crossrefs

Cf A337115, A347333, A344660, A344659.

Sequence in context: A136695 A337115 A354372 * A154129 A176014 A011447

Adjacent sequences: A354108 A354109 A354110 * A354112 A354113 A354114

Keyword

nonn,base

Author

Scott R. Shannon and Eric Angelini, May 17 2022

Status

approved