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A272386 Smallest primes of 5 X 5 magic squares formed from consecutive primes. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 23 12:24 EDT 2019. Contains 326222 sequences. (Running on oeis4.)