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

Author

Arkadiusz Wesolowski, Apr 28 2016

Keywords

• nonn

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

Examples

			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|
|----|----|----|----|----|
		

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

Crossrefs

Cf. A176571, A256891, A260673, A272387.

Programs

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