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

%I A270305 #16 Feb 16 2025 08:33:31
%S A270305 4440084513,5551770297,15588557967,16804701687,17271853617,
%T A270305 18145113213,18453231933,28551366903,57156707667,61433605083,
%U A270305 71440079091,72080670603,80244450939,85559974287,104463978483,133262909853,147857315253,221483397153,221924345793,222661558173,229451723637,229680831153,240429269013,257676075807,267398777427,286546347237,299932274193
%N A270305 Magic sums of 3 X 3 magic squares composed of consecutive primes.
%D A270305 Allan W. Johnson, Jr., Consecutive-Prime Magic Squares, Journal of Recreational Mathematics, vol. 15, 1982-83, pp. 17-18.
%D A270305 H. L. Nelson, A Consecutive Prime 3 x 3 Magic Square, Journal of Recreational Mathematics, vol. 20:3, 1988, p. 214.
%H A270305 A.H.M. Smeets, <a href="/A270305/b270305.txt">Table of n, a(n) for n = 1..759</a>
%H A270305 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeMagicSquare.html">Prime Magic Square</a>
%H A270305 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%F A270305 a(n) = 3*A166113(n).
%F A270305 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
%F A270305 a(n) = 3*A256891(n) + 9*A343194(n) + 3*A343195(n). - _A.H.M. Smeets_, Apr 08 2021
%o A270305 (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 A270305 Cf. A073519, A073520, A166113, A173981, A256891, A343194, A343195.
%Y A270305 Subsequence of A268912.
%K A270305 nonn
%O A270305 1,1
%A A270305 _Arkadiusz Wesolowski_, Mar 14 2016