A053999 Prime number spiral (clockwise, Northwest spoke).

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

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

Ivan Panchenko, Table of n, a(n) for n = 0..1000

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

Cf. A016754, A054551, A054553, A054555, A054564, A054566, A054566, A054570.

Sequence in context: A270868 A239186 A238185 * A357739 A131176 A141405

Adjacent sequences: A053996 A053997 A053998 * A054000 A054001 A054002

Keyword

easy,nonn

Author

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

Extensions

Edited by Robert G. Wilson v, Feb 25 2002

Status

approved