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 A177434 The magic constants of 6 X 6 magic squares composed of consecutive primes. 7
 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) FORMULA a(n) = Sum_{k=0..35} A000040(A000720(A272387(n))+k)/6. - M. F. Hasler, Oct 28 2018 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 a 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] PROG (PARI) A177434(n, p=A272387[n], N=6)=sum(i=2, N^2, p=nextprime(p+1), p)/N \\ Uses a precomputed array A272387, but can actually be used to find the terms, cf A272387. - M. F. Hasler, Oct 28 2018 CROSSREFS Cf. A173981 (analog for 4 X 4), A176571 (analog for 5 X 5), A073523 (36 consecutive primes of a pandiagonal magic square), A073520 (smallest magic sum for n X n), A259733 (most-perfect 8 X 8), A272387 (smallest element of 6 X 6 magic squares of consecutive primes). Sequence in context: A288082 A251625 A156646 * A202444 A329872 A199330 Adjacent sequences: A177431 A177432 A177433 * A177435 A177436 A177437 KEYWORD nonn AUTHOR Natalia Makarova, May 08 2010 EXTENSIONS Edited by M. F. Hasler, Oct 28 2018 STATUS approved

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Last modified September 29 03:21 EDT 2023. Contains 365749 sequences. (Running on oeis4.)