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A270305 Magic sums of 3 X 3 magic squares composed of consecutive primes. 8


%S 4440084513,5551770297,15588557967,16804701687,17271853617,

%T 18145113213,18453231933,28551366903,57156707667,61433605083,

%U 71440079091,72080670603,80244450939,85559974287,104463978483,133262909853,147857315253,221483397153,221924345793,222661558173,229451723637,229680831153,240429269013,257676075807,267398777427,286546347237,299932274193

%N Magic sums of 3 X 3 magic squares composed of consecutive primes.

%D Allan W. Johnson, Jr., Consecutive-Prime Magic Squares, Journal of Recreational Mathematics, vol. 15, 1982-83, pp. 17-18.

%D H. L. Nelson, A Consecutive Prime 3 x 3 Magic Square, Journal of Recreational Mathematics, vol. 20:3, 1988, p. 214.

%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) = 3*A166113(n).

%F a(n) = Sum_{k=0..8} prime(pi(A256891(n))+k)/3, where (prime)pi = A000720, prime = A000040. A similar formula is possible using the central prime A166113(n). - _M. F. Hasler_, Oct 28 2018

%o (PARI) A270305(n,p=A256891[n],N=3)=sum(i=2,N^2,p=nextprime(p+1),p)/N \\ Illustrates the second formula. Uses a precomputed array A256891, unless the smallest prime is supplied as optional 2nd argument. See also the 4x4 and 5x5 analog, A173981 and A176571, where this is useful for finding possible sets of primes, cf. A260673 and A272386. - _M. F. Hasler_, Oct 28 2018

%Y Cf. A073519, A073520, A166113, A173981, A256891. Subsequence of A268912.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Mar 14 2016

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)