A054553 Prime number spiral (clockwise, Northeast spoke).

2, 5, 41, 127, 269, 467, 751, 1093, 1523, 2027, 2621, 3299, 4007, 4861, 5749, 6763, 7867, 9041, 10273, 11719, 13121, 14723, 16319, 18061, 19963, 21851, 23857, 26021, 28289, 30661, 33029, 35531, 38201, 40993, 43759, 46751, 49789, 52957, 56197

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

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

Examples

			Begin a prime number spiral at shell 0 (prime 2), proceed clockwise, Northeast.
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. A000040, A054554, A054551, A054555, A054564, A054566, A054568, A054570, A053999.

Programs

Magma

[NthPrime(4*n^2 - 10*n + 7): n in [1..40]]; // Vincenzo Librandi, Aug 29 2018

Mathematica

Table[ Prime[4n^2 - 10n + 7], {n, 1, 40} ]

Formula

a(n) = A000040(A054554(n+1)). - R. J. Mathar, Aug 29 2018

Extensions

Edited by Robert G. Wilson v, Feb 25 2002