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A055390
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Terms of A007634 where n - 40 is not a square.
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5
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81, 82, 84, 87, 91, 96, 102, 109, 117, 122, 123, 126, 127, 130, 136, 138, 143, 147, 155, 159, 162, 163, 164, 170, 172, 173, 178, 185, 186, 187, 190, 201, 204, 205, 207, 208, 213, 215, 216, 217, 218, 232, 234, 237, 239, 242, 244, 245, 246, 248, 249, 251, 252
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OFFSET
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1,1
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COMMENTS
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Note that if h(n) = n^2 + n + 41, and k(x) = x^2 + 40, then the composition of functions h(k(x)) has an algebraic factorization: h(k(x)) = (x^2 + 40)^2 + (x^2 + 40) + 41 = (x^2 + x + 41)*(x^2 - x + 41). Since both of the expressions in the above product are integers greater than 1, h(k(x)) is composite. - Matt C. Anderson, Oct 24 2012
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LINKS
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FORMULA
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MAPLE
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for n from 0 to 1000 do
k := n^2+n+41:
end do:
pv1 := Vector(1000, j -> (j-1)^2+40):
p1 := convert(pv1, set):
remove(t -> issqr(t-40) or isprime(t^2+t+41), [$1..1000]); # Robert Israel, Nov 24 2017
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MATHEMATICA
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Select[Range[260], CompositeQ[#^2+#+41]&&!IntegerQ[Sqrt[#-40]]&] (* Harvey P. Dale, Oct 20 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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