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Initial member of 8 consecutive primes a, b, c, d, e, f, g, h such that (a + h) = (b + g), (c + g) = (d + f), (a + f) = (b + e) and (a + g) = (b + f).
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%I #18 Nov 03 2017 14:23:10

%S 6337,14717,77521,83401,130643,344231,357653,380377,496453,505067,

%T 587101,593473,970457,1130251,1515691,1694191,1936741,2689997,2773007,

%U 2811163,3665371,3678887,3713993,3976361,4024687,4181579,4629461,4801673,5438569,5882197,6016811

%N Initial member of 8 consecutive primes a, b, c, d, e, f, g, h such that (a + h) = (b + g), (c + g) = (d + f), (a + f) = (b + e) and (a + g) = (b + f).

%C The equations reduce to b-a = d-c = f-e = g-f = h-g, i.e. gap number 1, 3, 5, 6, 7 are equal. - _Jens Kruse Andersen_, Oct 14 2017

%H Harvey P. Dale, <a href="/A292715/b292715.txt">Table of n, a(n) for n = 1..230</a>

%e 6337 is a term because it is the first of 8 consecutive primes {6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379} = {a, b, c, d, e, f, g, h}; and (a + h) = (b + g), (c + g) = (d + f), (a + f) = (b + e) and (a + g) = (b + f).

%p A292715:= proc(n)local a, b, c, d, e, f, g, h; a:=ithprime(n); b:=ithprime(n + 1); c:=ithprime(n + 2); d:=ithprime(n + 3); e:=ithprime(n + 4); f:=ithprime(n + 5); g:=ithprime(n + 6); h:=ithprime(n + 7); if (a + h) = (b + g) and (c + g) = (d + f) and (a + f) = (b + e) and (a + g)=(b + f) then RETURN (a); fi; end: seq(A292715(n), n=1..1000000);

%t Select[Partition[Prime@ Range[10^6], 8, 1], Function[{a, b, c, d, e, f, g, h}, And[(a + h) == (b + g), (c + g) == (d + f), (a + f) == (b + e), (a + g) == (b + f)]] @@ # &][[All, 1]] (* _Michael De Vlieger_, Sep 21 2017 *)

%t Select[Partition[Prime[Range[420000]],8,1],Length[Union[Drop[Drop[ Differences[ #],{4}],{2}]]]==1&][[All,1]](* _Harvey P. Dale_, Nov 03 2017 *)

%Y Cf. A000040, A292618.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Sep 21 2017