A272386 Smallest primes of 5 X 5 magic squares formed from consecutive primes.

13, 59, 79, 97, 107, 127, 157, 269, 337, 347, 439, 457, 479, 563, 601, 631, 719, 743, 883, 947, 1021, 1031, 1049, 1051, 1061, 1093, 1109, 1171, 1201, 1223, 1499, 1523, 1601, 1669, 1811, 1901, 1933, 1997, 2011, 2053, 2153, 2207, 2341, 2399, 2531, 2539, 2549, 2551

Offset

1,1

Comments

A necessary condition for a prime being in this sequence is that the sum of this and the subsequent 24 primes divided by 5 must be an odd integer. - M. F. Hasler, Oct 30 2018

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..66

Eric Weisstein's World of Mathematics, Prime Magic Square

Arkadiusz Wesolowski, Examples of these magic squares

Index entries for sequences related to magic squares

Example

The smallest 5 X 5 magic square that can be formed from 25 consecutive primes consists of the primes 13 through 113, so the first term is 13:
           n = 1
|----|----|----|----|----|
| 13 | 107| 73 | 101| 19 |
|----|----|----|----|----|
| 97 | 17 | 79 | 37 | 83 |
|----|----|----|----|----|
| 41 | 53 | 109| 43 | 67 |
|----|----|----|----|----|
| 103| 89 | 29 | 61 | 31 |
|----|----|----|----|----|
| 59 | 47 | 23 | 71 | 113|
|----|----|----|----|----|
The next smallest consists of the primes 59 through 179, so the second term is 59:
          n = 2
|----|----|----|----|----|
| 59 | 163| 151| 137| 67 |
|----|----|----|----|----|
| 149| 61 | 79 | 109| 179|
|----|----|----|----|----|
| 113| 83 | 173| 107| 101|
|----|----|----|----|----|
| 167| 139| 71 | 127| 73 |
|----|----|----|----|----|
| 89 | 131| 103| 97 | 157|
|----|----|----|----|----|

Prog

(PARI) A272386(n)=MagicPrimes(A176571(n), 5)[1] \\ See A073519 for MagicPrimes(). - M. F. Hasler, Oct 28 2018
(PARI) is_candidate(p)={denominator(p=A173981(, p))==1 && bittest(p, 0)} \\ For p < 167, this yields exactly the terms of A272386. Exceptions (primes satisfying this but not in A272386) are (167, 227, 383, 461, 607, ...). - M. F. Hasler, Oct 30 2018

Crossrefs

Cf. A176571, A256891, A260673, A272387.

Sequence in context: A055833 A103220 A086221 * A171749 A141917 A163833

Adjacent sequences: A272383 A272384 A272385 * A272387 A272388 A272389

Keyword

nonn

Author

Arkadiusz Wesolowski, Apr 28 2016

Status

approved