A072359 - OEIS

A072359

Primes p such that the p-1 digits of the decimal expansion of k/p (for k=1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.

%I #19 Oct 13 2022 13:03:55

%S 19,383,32327,34061,45341,61967,65699,117541,158771,405817,444287,

%T 456503,695389,724781,1102567,1177859,1498139,2336989,2695337,3036857,

%U 3249419,3512749,3571429,4427299,5141051,7033823,8324411,9932179

%N Primes p such that the p-1 digits of the decimal expansion of k/p (for k=1,2,3,...,p-1) fit into the k-th row of a magic square grid of order p-1.

%D W. S. Andrews, Magic Squares and Cubes, pp. 176 Dover NY 1960.

%D J. Heleen, Journal of Recreational Mathematics, 30(1) 1999-2000 pp. 72-3 Soln. to Prob. 2394. Magic Reciprocals

%D M. J. Zerger, Journal of Recreational Mathematics, 30(2) 1999-2000 pp. 158-160 Soln. to Prob. 2420. Only 19?

%H Harvey Heinz, <a href="http://recmath.org/Magic%20Squares/magicsquare.htm#Order-19%20based%20on%201/19">Order-18 based on 1/19</a>

%H Simon Whitechapel, <a href="https://web.archive.org/web/20080518020634/http://www.gwywyr.com/articles/scimaths/pseudo.html">Reciprocal Arrangements</a> [Internet Archive Wayback Machine]

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_reciprocal_magic_square">Prime reciprocal magic square</a>

%Y Cf. A021023 (1/19), A021387 (1/383), A096339, A096660.

%K nonn,base

%O 1,1

%A _Lekraj Beedassy_, Jul 18 2002

%E More terms from _William Rex Marshall_, Aug 18 2005