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A053999 Prime number spiral (clockwise, Northwest spoke). 9
2, 23, 97, 227, 419, 661, 1009, 1427, 1879, 2437, 3083, 3803, 4637, 5519, 6481, 7573, 8737, 9931, 11321, 12743, 14327, 15877, 17609, 19471, 21391, 23327, 25469, 27739, 30047, 32429, 34849, 37501, 40231, 42943, 45989, 49037, 52121, 55381, 58579 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Largest prime in n-th shell of prime spiral.
Shell 1 comprises the primes 3 5 7 11 13 17 19 23; 3 is lowest, 23 is highest.
LINKS
FORMULA
8-spoke wheel overlays prime number spiral; hub is 2 in shell 0; 8 spokes radiate from this hub; this is Northwest, clockwise.
a(n) = A000040(A016754(n)) . - R. J. Mathar, Aug 29 2018
EXAMPLE
Begin a prime number spiral at shell 0 (prime 2), proceed clockwise, Northwest.
From Omar E. Pol, Feb 19 2022: (Start)
The spiral with four terms in every spoke looks like this:
.
227 101--103--107--109--113--127
| | |
223 97 29---31---37---41 131
| | | | |
211 89 23 3----5 43 137
| | | | | | |
199 83 19 2 7 47 139
| | | | | |
197 79 17---13---11 53 149
| | | |
193 73---71---67---61---59 151
| |
191--181--179--173--167--163--157
.
(End)
MATHEMATICA
Table[ Prime[4n^2 + 4n + 1], {n, 0, 40} ]
CROSSREFS
Sequence in context: A270868 A239186 A238185 * A357739 A131176 A141405
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Edited by Robert G. Wilson v, Feb 25 2002
STATUS
approved

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Last modified February 21 03:04 EST 2024. Contains 370219 sequences. (Running on oeis4.)