A054570 - OEIS

%I #21 Feb 19 2022 12:49:53

%S 2,19,83,199,389,641,967,1361,1823,2377,3001,3709,4517,5419,6353,7477,

%T 8623,9791,11159,12577,14083,15667,17417,19273,21149,23063,25229,

%U 27431,29683,32183,34543,37171,39877,42641,45599,48673,51719,54973,58171

%N Prime number spiral (clockwise, West spoke).

%H Ivan Panchenko, <a href="/A054570/b054570.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = A000040(A033951(n)). - _R. J. Mathar_, Aug 29 2018

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

%e From _Omar E. Pol_, Feb 19 2022: (Start)

%e The spiral with four terms in every spoke looks like this:

%e .

%e   227  101--103--107--109--113--127

%e    |     |                       |

%e   223   97   29---31---37---41  131

%e    |     |    |              |   |

%e   211   89   23    3----5   43  137

%e    |     |    |    |    |    |   |

%e   199   83   19    2    7   47  139

%e    |     |    |         |    |   |

%e   197   79   17---13---11   53  149

%e    |     |                   |   |

%e   193   73---71---67---61---59  151

%e    |                             |

%e   191--181--179--173--167--163--157

%e .

%e (End)

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

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

%K easy,nonn

%O 0,1

%A _Enoch Haga_ and _G. L. Honaker, Jr._, Apr 10 2000

%E Edited by _Frank Ellermann_, Feb 24 2002