A054551 Prime number spiral (clockwise, North spoke).

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

Offset: 0

Author

Enoch Haga and G. L. Honaker, Jr. Apr 09 2000

Keywords

• easy
• nonn

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.

Examples

			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)
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Hermetic Systems, Prime Number Spiral.

Crossrefs

Cf. A000040, A054552, A054553, A054555, A054564, A054566, A054568, A054570, A053999.

Programs

Mathematica

Table[ Prime[4n^2 - 3n + 1], {n, 0, 40} ]

Formula

a(n) = A000040(A054552(n)). - R. J. Mathar, Aug 29 2018

Extensions

Edited by Robert G. Wilson v, Feb 25 2002