A073519 The set of nine consecutive primes forming a 3 X 3 magic square with the smallest magic constant (4440084513).

1480028129, 1480028141, 1480028153, 1480028159, 1480028171, 1480028183, 1480028189, 1480028201, 1480028213

Offset

1,1

Comments

The square is given (with the terms in correct order) in A320873. The (increasingly ordered) set of primes does not contain more information than the magic constant (= sum) S, since they have to be consecutive and sum up to 3*S. It is easy to construct the unique set of (consecutive) primes with this property, cf. PROGRAM. - M. F. Hasler, Oct 28 2018

References

H. L. Nelson, Journal of Recreational Mathematics, 1988, vol. 20:3, p. 214.

Clifford A. Pickover, The Zen of Magic Squares, Circles and Stars: An Exhibition of Surprising Structures across Dimensions, Princeton University Press, 2002.

Links

Table of n, a(n) for n=1..9.

Harvey D. Heinz, Prime Numbers Magic Squares: Minimum consecutive primes - 3, 1999-2010.

Index entries for sequences related to magic squares

Example

The magic square is
[ 1480028201 1480028129 1480028183 ]
[ 1480028153 1480028171 1480028189 ]
[ 1480028159 1480028213 1480028141 ]

Prog

(PARI) A073519=MagicPrimes(4440084513, 3) \\ where: (also used in A073521, ...)
MagicPrimes(S, n, P=[nextprime(S\n)])={S=n*S-P[1]; for(i=1, -1+n*=n, S-=if(S>(n-i)*P[1], P=concat(P, nextprime(P[#P]+1)); P[#P], P=concat(precprime(P[1]-1), P); P[1])); if(S, -P, P)} \\ The vector of n^2 primes whose sum is n*S, or a negative vector with an approximate solution if no exact solution exists. - M. F. Hasler, Oct 22 2018

Crossrefs

Cf. A024351, A073520, A073521, A073522, A073523, A256891, A265139, A265614.

Sequence in context: A372106 A048051 A345337 * A256891 A320873 A166113

Adjacent sequences: A073516 A073517 A073518 * A073520 A073521 A073522

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Aug 29 2002

Status

approved