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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.

%I A292618 #27 Sep 21 2017 08:05:22
%S A292618 359,389,839,853,937,1019,2213,2221,2237,2593,3019,3821,3823,4111,
%T A292618 4231,4801,5407,5839,6997,12241,13499,14741,15473,25603,25771,25793,
%U A292618 26393,28597,29297,30839,31147,31543,35051,40487,45281,47933,50023,51827,55061,55441,60343
%N 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.
%C A292618 In this condition, we can draw the following graphic whose sides are primes.
%C A292618                      c
%C A292618                  *------*
%C A292618                  |      |
%C A292618                 d|      |b
%C A292618           e      |  *---*
%C A292618     *------------*  | a
%C A292618     |               |
%C A292618     |               |
%C A292618     |               |
%C A292618    f|               |h
%C A292618     |               |
%C A292618     |     g         |
%C A292618     *---------------*
%C A292618 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
%H A292618 Seiichi Manyama, <a href="/A292618/b292618.txt">Table of n, a(n) for n = 1..10000</a>
%H A292618 Números y algo mas's blog, <a href="http://simplementenumeros.blogspot.jp/2014/05/1315-goligonos-goliedros-y-demas.html">1315 - Golígonos, Goliedros y demás</a>.
%e A292618 If a = 359, b, c, d, e, f, g, h = 367, 373, 379, 383, 389, 397, 401.
%p A292618 Primes:= select(isprime, [2,seq(i,i=3..10^5,2)]):
%p A292618 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])];
%p A292618 # _Robert Israel_, Sep 20 2017
%o A292618 (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
%K A292618 nonn
%O A292618 1,1
%A A292618 _Seiichi Manyama_, Sep 20 2017