A054570 Prime number spiral (clockwise, West spoke).

2, 19, 83, 199, 389, 641, 967, 1361, 1823, 2377, 3001, 3709, 4517, 5419, 6353, 7477, 8623, 9791, 11159, 12577, 14083, 15667, 17417, 19273, 21149, 23063, 25229, 27431, 29683, 32183, 34543, 37171, 39877, 42641, 45599, 48673, 51719, 54973, 58171

Offset: 0

Author

Enoch Haga and G. L. Honaker, Jr., Apr 10 2000

Keywords

• easy
• nonn

Examples

			Begin a prime number spiral at shell 0 (prime 2), proceed clockwise, West.
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

Crossrefs

Cf. A033951, A054551, A054553, A054555, A054564, A054566, A054570, A053999.

Programs

Mathematica

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

Formula

8-spoke wheel overlays prime number spiral; hub is 2 in shell 0; 8 spokes radiate from this hub; this is West, clockwise.

a(n) = A000040(A033951(n)). - R. J. Mathar, Aug 29 2018

Extensions

Edited by Frank Ellermann, Feb 24 2002