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Magic sums of 4 X 4 semimagic squares composed of primes.
1

%I #7 Apr 29 2016 23:39:18

%S 114,120,124,126,130,132,136,138,140,142,144,146,148,150,152,154,156,

%T 158,160,162,164,166,168,170,172,174,176,178,180,182,184,186,188,190,

%U 192,194,196,198,200,202,204,206,208,210,212,214,216,218,220,222,224,226

%N Magic sums of 4 X 4 semimagic squares composed of primes.

%C In other words, numbers n such that there is a 4 X 4 semimagic square of primes with magic sum n.

%C Conjecture: every even number greater than 134 belongs to this sequence.

%H Arkadiusz Wesolowski, <a href="/A272303/b272303.txt">Table of n, a(n) for n = 1..189</a>

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

%F If conjecture is true, a(n) = A005843(n+61) for n >= 7.

%e Examples of 4 X 4 semimagic squares composed of primes.

%e .

%e |---|---|---|---|

%e | 3 | 11| 47| 53|

%e |---|---|---|---|

%e | 23| 37| 41| 13|

%e |---|---|---|---|

%e | 29| 61| 7 | 17|

%e |---|---|---|---|

%e | 59| 5 | 19| 31|

%e |---|---|---|---|

%e The magic constant is 114 = a(1).

%e .

%e |---|---|---|---|

%e | 3 | 5 | 23| 89|

%e |---|---|---|---|

%e | 17| 53| 37| 13|

%e |---|---|---|---|

%e | 41| 43| 29| 7 |

%e |---|---|---|---|

%e | 59| 19| 31| 11|

%e |---|---|---|---|

%e The magic constant is 120 = a(2).

%Y Cf. A270864. Supersequence of A271578.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Apr 25 2016