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A308412 Indices of Gaussian primes on a square spiral. 1

%I

%S 3,5,7,9,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,

%T 52,54,60,62,68,70,76,78,82,84,88,90,92,94,98,100,102,104,108,110,112,

%U 114,118,120,122,126,128,132,134,138,140,144,146,150,152,156,158

%N Indices of Gaussian primes on a square spiral.

%C These are the numbers k > 0 such that A174344(k) + i*A274923(k) is a Gaussian prime (where i denotes the imaginary unit).

%C For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.

%C All terms except the first four are even.

%H Rémy Sigrist, <a href="/A308412/a308412_1.gp.txt">PARI program for A308412</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianPrime.html">Gaussian Prime</a>

%e The first terms displayed on the center of a counterclockwise square spiral are:

%e y\x| -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5

%e ---+--------------------------------------------------------

%e +5| *--100----*---98----*----*----*---94----*---92----*

%e | | |

%e +4| 102 *----*----*---62----*---60----*----*----* 90

%e | | | | |

%e +3| * * *---36----*---34----*---32----* * *

%e | | | | | | |

%e +2| 104 * 38 *---16----*---14----* 30 * 88

%e | | | | | | | | |

%e +1| * 68 * 18 5----*----3 12 * 54 *

%e | | | | | | | | | | |

%e 0| * * 40 * * *----* * 28 * *

%e | | | | | | | | | |

%e -1| * 70 * 20 7----*----9---10 * 52 *

%e | | | | | | | |

%e -2| 108 * 42 *---22----*---24----*---26 * 84

%e | | | | | |

%e -3| * * *---44----*---46----*---48----*----* *

%e | | | |

%e 4| 110 *----*----*---76----*---78----*----*----*---82

%e | |

%e 5| *--112----*--114----*----*----*--118----*--120----*

%o (PARI) See Links section.

%Y Cf. A174344, A274923.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Jun 01 2019

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Last modified December 2 03:22 EST 2020. Contains 338865 sequences. (Running on oeis4.)