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

1,3

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

.

Links

Table of n, a(n) for n=1..77.

Example

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.

Sequence in context: A228799 A329499 A220393 * A109847 A260059 A122459

Adjacent sequences: A344656 A344657 A344658 * A344660 A344661 A344662

Keyword

nonn

Author

Eric Angelini and Scott R. Shannon, May 26 2021

Status

approved