A344659 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that each term forms no prime value in the eight sums when each term is added to each of its eight nearest neighbors.

0, 1, 8, 14, 4, 6, 9, 15, 20, 5, 7, 13, 2, 12, 10, 11, 16, 22, 18, 3, 17, 19, 25, 29, 28, 21, 23, 27, 31, 26, 24, 30, 32, 34, 35, 33, 36, 41, 40, 42, 39, 37, 38, 43, 45, 47, 49, 53, 57, 48, 51, 54, 61, 50, 44, 46, 52, 56, 58, 60, 59, 65, 55, 62, 63, 70, 64, 74, 66, 69, 67, 68, 72, 73, 77, 71, 75

Offset: 1

Author

Eric Angelini and Scott R. Shannon, May 26 2021

Keywords

• nonn

Comments

.

36--33--35--34--32--30--24

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41 16--11--10--12---2 26

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40 22 4--14---8 13 31

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42 18 6 0---1 7 27

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39 3 9--15--20---5 23 .

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37 17--19--25--29--28--21 .

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38--43--45--47--49--53--57--48

.

Examples

			The eight terms that are in contact with the initial zero are 1, 8, 14, 4, 6, 9, 15, 20: none of them is prime [forcing the sum a(k) + 0 to be nonprime, with k<9]; more generally, no term of the square spiral when added to any of its eight nearest neighbors sums to a prime.
		

Crossrefs

Cf. A063826, A344660, A002808, A000040.