This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A177434 #25 Oct 31 2018 09:27:24
%S A177434 484,744,806,868,930,1390,1460,1494,1634,1704,1740,1848,1992,2100,
%T A177434 2172,2316,2390,2540,3116,3192,3694,3734,3774,4486,4946,4988,5736,
%U A177434 6104,6148,6526,6568,6610,6776,6820,6950,7036,7078,7120,7984,8118,8162,8828,9318
%N A177434 The magic constants of 6 X 6 magic squares composed of consecutive primes.
%C A177434 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).
%C A177434 Each of the first 100 possible arrays of 36 consecutive primes which satisfy the necessary condition produces a magic square.
%C A177434 A program written by Stefano Tognon was used.
%H A177434 Natalya Makarova, <a href="http://www.natalimak1.narod.ru/mk6pr.htm">Author's webpage (in Russian)</a>
%F A177434 a(n) = Sum_{k=0..35} A000040(A000720(A272387(n))+k)/6. - _M. F. Hasler_, Oct 28 2018
%e A177434 S = 744
%e A177434 [139 113 151 131 83 127]
%e A177434 [223 149 89 47 157 79]
%e A177434 [173 103 181 167 59 61]
%e A177434 [ 67 137 53 97 211 179]
%e A177434 [101 199 73 109 71 191]
%e A177434 [ 41 43 197 193 163 107]
%e A177434 S = 806
%e A177434 [131 53 107 157 191 167]
%e A177434 [ 89 229 179 97 109 103]
%e A177434 [ 83 211 71 139 79 223]
%e A177434 [113 101 137 181 227 47]
%e A177434 [197 61 163 59 127 199]
%e A177434 [193 151 149 173 73 67]
%e A177434 S = 868
%e A177434 [191 137 79 193 197 71]
%e A177434 [ 67 157 73 229 239 103]
%e A177434 [179 173 167 97 101 151]
%e A177434 [211 181 223 61 109 83]
%e A177434 [113 131 199 139 59 227]
%e A177434 [107 89 127 149 163 233]
%e A177434 Magic square with S=930 can be pan-diagonal (cf. A073523).
%e A177434 Example of a non-pan-diagonal square:
%e A177434 S = 930
%e A177434 [167 71 151 199 131 211]
%e A177434 [ 89 241 181 73 113 233]
%e A177434 [ 83 227 127 197 229 67]
%e A177434 [239 137 139 103 163 149]
%e A177434 [179 97 223 251 101 79]
%e A177434 [173 157 109 107 193 191]
%o A177434 (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
%Y A177434 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).
%K A177434 nonn
%O A177434 1,1
%A A177434 _Natalia Makarova_, May 08 2010
%E A177434 Edited by _M. F. Hasler_, Oct 28 2018