A347333 -id:A347333 - cp's OEIS frontend

A347334 Successive prime sums of the squares forming A347333.

17, 71, 223, 563, 1213, 2027, 2879, 5393, 7537, 10973, 16087, 18587, 26539, 34319, 46133, 60937, 70687, 87103, 110221, 132911, 165779, 203051, 215461, 262897, 318431, 347209, 411779, 487603, 539039, 597209, 695999, 806543, 874403, 998969, 1078111, 1233073, 1327489, 1509581, 1697461, 1804841, 2029369

Offset: 1

Eric Angelini and Scott R. Shannon, Aug 28 2021

Note that the terms are not constantly increasing; the first term which decreases is a(51) = 4296709, which is less than a(50) = 4357201. The first consecutive terms that are equal are a(65) = a(66) = 11893993.

Scott R. Shannon, Table of n, a(n) for n = 1..200.

Cf. A347333.

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.

Original entry on oeis.org

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

Scott R. Shannon and Eric Angelini, May 17 2022

			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;

Cf A337115, A347333, A344660, A344659.

cp's OEIS Frontend

A347334 Successive prime sums of the squares forming A347333.

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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.

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