A054564 Prime number spiral (clockwise, Southeast spoke).

2, 11, 59, 157, 313, 547, 829, 1201, 1621, 2153, 2749, 3463, 4217, 5059, 6011, 7001, 8167, 9343, 10631, 12071, 13513, 15107, 16759, 18481, 20399, 22343, 24371, 26591, 28807, 31231, 33617, 36229, 38891, 41647, 44501, 47533, 50549, 53759, 56957

Offset

0,1

Comments

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

Links

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

Formula

a(n) = A000040(A053755(n)). - R. J. Mathar, Aug 29 2018

Example

Begin a prime number spiral at shell 0 (prime 2), proceed clockwise, Southeast.
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 + 1], {n, 0, 40} ]

Crossrefs

Cf. A053755, A054551, A054553, A054555, A054566, A054568, A054570, A053999.

Sequence in context: A020057 A363646 A210646 * A280674 A139172 A228868

Adjacent sequences: A054561 A054562 A054563 * A054565 A054566 A054567

Keyword

easy,nonn

Author

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

Extensions

Edited by Frank Ellermann, Feb 24 2002

Status

approved