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A292618 The first prime of 8 consecutive primes a, b, c, d, e, f, g, h such that a + g = c + e and b + h = d + f. 5
359, 389, 839, 853, 937, 1019, 2213, 2221, 2237, 2593, 3019, 3821, 3823, 4111, 4231, 4801, 5407, 5839, 6997, 12241, 13499, 14741, 15473, 25603, 25771, 25793, 26393, 28597, 29297, 30839, 31147, 31543, 35051, 40487, 45281, 47933, 50023, 51827, 55061, 55441, 60343 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In this condition, we can draw the following graphic whose sides are primes.

                     c

                 *------*

                 |      |

                d|      |b

          e      |  *---*

    *------------*  | a

    |               |

    |               |

    |               |

   f|               |h

    |               |

    |     g         |

    *---------------*

Dickson's conjecture implies that there are infinitely many prime octuplets of forms such as x, x+4, x+10, x+12, x+18, x+22, x+28, x+30, and thus infinitely many members of the sequence. - Robert Israel, Sep 20 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Números y algo mas's blog, 1315 - Golígonos, Goliedros y demás.

EXAMPLE

If a = 359, b, c, d, e, f, g, h = 367, 373, 379, 383, 389, 397, 401.

MAPLE

Primes:= select(isprime, [2, seq(i, i=3..10^5, 2)]):

Primes[select(i -> Primes[i]+Primes[i+6] = Primes[i+2]+Primes[i+4] and Primes[i+1]+Primes[i+7]=Primes[i+3]+Primes[i+5], [$1..nops(Primes)-7])];

# Robert Israel, Sep 20 2017

PROG

(PARI) forprime(p=1, 61000, my(v=primes([p, nextprime(nextprime(nextprime(nextprime(nextprime(nextprime(nextprime(p+1)+1)+1)+1)+1)+1)+1)])); if(v[1]+v[7]==v[3]+v[5] && v[2]+v[8]==v[4]+v[6], print1(p, ", "))) \\ Felix Fröhlich, Sep 20 2017

CROSSREFS

Sequence in context: A280403 A145533 A273806 * A186461 A142381 A054826

Adjacent sequences:  A292615 A292616 A292617 * A292619 A292620 A292621

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 20 2017

STATUS

approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)