A343195 - OEIS

%I #20 Jun 08 2021 06:26:29

%S 6,6,6,6,6,6,6,6,6,6,-6,6,24,6,6,6,-18,6,6,-18,6,6,-18,6,-18,6,24,6,6,

%T -6,6,-18,6,24,6,6,6,6,-18,6,6,-54,-18,6,6,6,-18,12,6,78,12,-18,24,24,

%U -24,6,6,6,6,6,24,6,6,6,6,12,12,24,6,6,24,-18,6,24

%N a(n) is the parameter c in the three parameter description of 3 X 3 magic squares of consecutive primes (see comment).

%C Each 3 X 3 magic square of consecutive primes can be described by three parameters: p1, b and c, where p1 is the smallest prime in the magic square, b > 0 and c > -b; the magic square is then given by:

%C   +----------+----------+----------+

%C   | p1+5b+2c | p1       | p1+4b+c  |

%C   +----------+----------+----------+

%C   | p1+2b    | p1+3b+c  | p1+4b+2c |

%C   +----------+----------+----------+

%C   | p1+2b+c  | p1+6b+2c | p1+b     |

%C   +----------+----------+----------+

%C p1 is given in A256891 and b is given in A343194.

%C If c > 0, the magic square is of type 1; if -b < c < 0, the magic square is of type 2. If the consecutive primes are given by p1, p2, ..., p9 (in increasing order), the magic square types are given by:

%C   Type 1             Type 2

%C   +----+----+----+   +----+----+----+

%C   | p8 | p1 | p6 |   | p8 | p1 | p7 |

%C   +----+----+----+   +----+----+----+

%C   | p3 | p5 | p7 |   | p4 | p5 | p6 |

%C   +----+----+----+   +----+----+----+

%C   | p4 | p9 | p2 |   | p3 | p9 | p2 |

%C   +----+----+----+   +----+----+----+

%H A.H.M. Smeets, <a href="/A343195/b343195.txt">Table of n, a(n) for n = 1..759</a>

%H Harvey D. Heinz, <a href="http://www.magic-squares.net/primesqr.htm#Minimum consecutive primes -3">Prime Numbers Magic Squares: Minimum consecutive primes - 3</a>, 1999-2010.

%H A.H.M. Smeets, <a href="/A343195/a343195.txt">Python program</a>

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

%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>

%F a(n) = (A270305(n) - 3*A256891(n) - 9*A343194(n))/3.

%F a(n) = A166113(n) - A256891(n) - 3*A343194(n).

%Y Cf. A166113 (p5), A256891 (p1), A270305 (magic constant), A343194 (b).

%K sign

%O 1,1

%A _A.H.M. Smeets_, Apr 07 2021