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A344660 Lexicographically earliest sequence of distinct nonnegative terms on a square spiral such that each term, when written with one digit per square, forms no prime value in the eight sums when each digit is added to each of its eight nearest neighbors. 2
0, 1, 8, 80, 4, 6, 88, 7, 77, 2, 24, 40, 44, 22, 26, 27, 3, 5, 9, 72, 28, 42, 46, 48, 62, 64, 66, 68, 87, 13, 31, 37, 78, 82, 84, 86, 60, 400, 422, 222, 63, 601, 73, 33, 15, 35, 17, 10, 18, 224, 226, 404, 406, 424, 227, 286, 36, 99, 39, 19, 53, 55, 57, 59, 90, 93, 772, 228, 240, 408, 440, 426 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Terms are broken into digits before entering the spiral.
The sequence is finite. After 181 terms (and 466 digits) the number 101 is entered. The next square is surrounded by digits 0,1,8 so the only available digit is 8. As 8 has already appeared in the sequence another digit must be added to form a new number, but the next square is now surrounded with digits 0,1,3,8, and it is not possible to find a digit such that its sum with each of those digits is not prime.
.
4---0---4---6---2---2---4---2---2---8---1
| |
4 4---0---6---6---8---4---8---2---8 0
| | | |
. 0 4---6---4---2---4---8---2 8 1
. | | | | |
. 0 8 0---4---4---2---2 2 7 7
. | | | | | | |
. 4 6 4 0---8---8 7 7 7 1
. | | | | | | | | |
. 2 2 4 4 0---1 7 9 3 5
. | | | | | | | |
. 2 6 2 6---8---8---7 5 1 3
. | | | | | |
. 2 4 2---2---6---2---7---3 3 5
. | | | |
. 2 6---6---6---8---8---7---1---3 1
. | |
. 2---6---3---6---0---1---7---3---3---3
.
LINKS
EXAMPLE
The eight digits that are in contact with the initial zero are 1, 8, 8, 0, 4, 6, 8, 8: 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 added to any of its eight nearest neighbors sums to a prime.
CROSSREFS
Sequence in context: A034355 A289213 A201513 * A069022 A217401 A077333
KEYWORD
base,nonn,fini
AUTHOR
STATUS
approved

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Last modified June 17 12:36 EDT 2024. Contains 373445 sequences. (Running on oeis4.)