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

4440084513, 5551770297, 15588557967, 16804701687, 17271853617, 18145113213, 18453231933, 28551366903, 57156707667, 61433605083, 71440079091, 72080670603, 80244450939, 85559974287, 104463978483, 133262909853, 147857315253, 221483397153, 221924345793, 222661558173, 229451723637, 229680831153, 240429269013, 257676075807, 267398777427, 286546347237, 299932274193

Offset: 1

Author

Arkadiusz Wesolowski, Mar 14 2016

Keywords

• nonn

References

• Allan W. Johnson, Jr., Consecutive-Prime Magic Squares, Journal of Recreational Mathematics, vol. 15, 1982-83, pp. 17-18.
• H. L. Nelson, A Consecutive Prime 3 x 3 Magic Square, Journal of Recreational Mathematics, vol. 20:3, 1988, p. 214.

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..759
• Eric Weisstein's World of Mathematics, Prime Magic Square
• Index entries for sequences related to magic squares

Crossrefs

Cf. A073519, A073520, A166113, A173981, A256891, A343194, A343195.

Subsequence of A268912.

Programs

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

Formula

a(n) = 3*A166113(n).

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

a(n) = 3*A256891(n) + 9*A343194(n) + 3*A343195(n). - A.H.M. Smeets, Apr 08 2021