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

0,1

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

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

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

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

Sequence in context: A029973 A344736 A347332 * A049065 A274609 A128030

Adjacent sequences: A054548 A054549 A054550 * A054552 A054553 A054554

Keyword

easy,nonn

Author

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

Extensions

Edited by Robert G. Wilson v, Feb 25 2002

Status

approved