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A054551 Prime number spiral (clockwise, North spoke). 9
2, 3, 31, 107, 241, 443, 709, 1049, 1471, 1973, 2539, 3191, 3911, 4729, 5651, 6637, 7699, 8867, 10133, 11503, 12941, 14537, 16073, 17863, 19727, 21601, 23609, 25759, 27967, 30319, 32719, 35201, 37831, 40627, 43391, 46399, 49411, 52553, 55813 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Smallest prime in n-th shell of prime spiral.
8-spoke wheel overlays prime number spiral; hub is 2 in shell 0; 8 spokes radiate from this hub; this is North, clockwise.
Shell 1 comprises the primes 3 5 7 11 13 17 19 23; 3 is lowest, 23 is highest.
The wheel may be rotated, but the sequences though pointing in different directions, will remain the same.
LINKS
Hermetic Systems, Prime Number Spiral.
FORMULA
a(n) = A000040(A054552(n)). - R. J. Mathar, Aug 29 2018
EXAMPLE
Begin a prime number spiral at zero, proceed clockwise, North.
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 - 3n + 1], {n, 0, 40} ]
CROSSREFS
Sequence in context: A029973 A344736 A347332 * A049065 A274609 A128030
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Edited by Robert G. Wilson v, Feb 25 2002
STATUS
approved

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Last modified February 21 02:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)