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A336349
Square spiral of distinct positive integers constructed by greedy algorithm, such that all terms on the same row or on the same column are pairwise coprime.
3
1, 2, 3, 4, 5, 7, 6, 11, 13, 17, 9, 19, 8, 23, 15, 29, 31, 37, 25, 41, 12, 43, 47, 35, 53, 59, 49, 61, 67, 71, 10, 73, 79, 83, 89, 77, 27, 91, 97, 101, 95, 103, 16, 107, 109, 113, 121, 65, 51, 127, 131, 137, 139, 119, 149, 151, 18, 143, 157, 163, 133, 167, 173
OFFSET
1,2
COMMENTS
We can always extend the sequence with a prime number greater than any previous term, so the sequence is well defined.
For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.
LINKS
Rémy Sigrist, Colored representation of the spiral for -150 < x < 150 and -150 < y < 150 (where the hue is function of a(n))
Rémy Sigrist, Colored representation of the spiral for -150 < x < 150 and -150 < y < 150 (where black pixels correspond to prime numbers)
EXAMPLE
The spiral begins:
85--179--173--167--133--163--157--143---18
| |
169 27---77---89---83---79---73---10 151
| | | |
181 91 31---29---15---23----8 71 149
| | | | | |
191 97 37 5----4----3 19 67 119
| | | | | | | |
193 101 25 7 1----2 9 61 139
| | | | | | |
197 95 41 6---11---13---17 49 137
| | | | |
199 103 12---43---47---35---53---59 131
| | |
161 16--107--109--113--121---65---51--127
|
22--211--221--223--227--229--203--233--115
PROG
(PARI) See Links section.
CROSSREFS
See A336350 for a similar sequence.
Sequence in context: A080688 A082025 A076034 * A255545 A034152 A344316
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 19 2020
STATUS
approved