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A292715
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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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4
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6337, 14717, 77521, 83401, 130643, 344231, 357653, 380377, 496453, 505067, 587101, 593473, 970457, 1130251, 1515691, 1694191, 1936741, 2689997, 2773007, 2811163, 3665371, 3678887, 3713993, 3976361, 4024687, 4181579, 4629461, 4801673, 5438569, 5882197, 6016811
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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).
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MAPLE
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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);
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MATHEMATICA
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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 *)
Select[Partition[Prime[Range[420000]], 8, 1], Length[Union[Drop[Drop[ Differences[ #], {4}], {2}]]]==1&][[All, 1]](* Harvey P. Dale, Nov 03 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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