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A177434 The magic constants of 6 X 6 magic squares composed of consecutive primes. 5
484, 744, 806, 868, 930, 1390, 1460, 1494, 1634, 1704, 1740, 1848, 1992, 2100, 2172, 2316, 2390, 2540, 3116, 3192, 3694, 3734, 3774, 4486, 4946, 4988, 5736, 6104, 6148, 6526, 6568, 6610, 6776, 6820, 6950, 7036, 7078, 7120, 7984, 8118, 8162, 8828, 9318 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let Z be a sum of 36 consecutive primes. A necessary condition to get a 6 X 6 magic square using these primes is that Z=6S, where S is even. The smallest magic constant of a 6 X 6 magic square of consecutive primes is 484 (cf. A073520).

Each of the first 100 possible arrays of 36 consecutive primes which satisfy the necessary condition produces a magic square.

A program written by Stefano Tognon was used.

LINKS

Table of n, a(n) for n=1..43.

Natalya Makarova, Author's webpage (in Russian)

EXAMPLE

S = 744

[139 113 151 131 83 127

223 149 89 47 157 79

173 103 181 167 59 61

67 137 53 97 211 179

101 199 73 109 71 191

41 43 197 193 163 107]

S = 806

[131 53 107 157 191 167

89 229 179 97 109 103

83 211 71 139 79 223

113 101 137 181 227 47

197 61 163 59 127 199

193 151 149 173 73 67]

S = 868

[191 137 79 193 197 71

67 157 73 229 239 103

179 173 167 97 101 151

211 181 223 61 109 83

113 131 199 139 59 227

107 89 127 149 163 233]

Magic square with S=930 can be pan-diagonal (cf. A073523).

Example of non pan-diagonal square:

S = 930

[167 71 151 199 131 211

89 241 181 73 113 233

83 227 127 197 229 67

239 137 139 103 163 149

179 97 223 251 101 79

173 157 109 107 193 191]

CROSSREFS

Cf. A173981, A176571, A073523, A073520, A259733, A272387.

Sequence in context: A158330 A251625 A156646 * A202444 A199330 A281398

Adjacent sequences:  A177431 A177432 A177433 * A177435 A177436 A177437

KEYWORD

nonn

AUTHOR

Natalia Makarova, May 08 2010

STATUS

approved

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Last modified May 23 06:42 EDT 2017. Contains 286909 sequences.