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A055390 Terms of A007634 where n - 40 is not a square.

%I A055390 #28 Nov 26 2017 13:59:10
%S A055390 81,82,84,87,91,96,102,109,117,122,123,126,127,130,136,138,143,147,
%T A055390 155,159,162,163,164,170,172,173,178,185,186,187,190,201,204,205,207,
%U A055390 208,213,215,216,217,218,232,234,237,239,242,244,245,246,248,249,251,252
%N A055390 Terms of A007634 where n - 40 is not a square.
%C A055390 Numbers n such that n^2 + n + 41 is composite and n - 40 is not a square. - _Charles R Greathouse IV_, Sep 14 2014
%C A055390 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
%H A055390 Robert Israel, <a href="/A055390/b055390.txt">Table of n, a(n) for n = 1..10000</a>
%F A055390 a(n) ~ n. - _Charles R Greathouse IV_, Sep 14 2014
%p A055390 A007634 := {}:
%p A055390 for n from 0 to 1000 do
%p A055390 k := n^2+n+41:
%p A055390 if isprime(k) = false then A007634 := union(A007634, {n}) end if:
%p A055390 end do:
%p A055390 pv1 := Vector(1000, j -> (j-1)^2+40):
%p A055390 p1 := convert(pv1, set):
%p A055390 A055390 := minus(A007634, p1); # _Matt C. Anderson_, Sep 26 2011
%p A055390 remove(t -> issqr(t-40) or isprime(t^2+t+41), [$1..1000]); # _Robert Israel_, Nov 24 2017
%t A055390 Select[Range[260],CompositeQ[#^2+#+41]&&!IntegerQ[Sqrt[#-40]]&] (* _Harvey P. Dale_, Oct 20 2015 *)
%o A055390 (PARI) is(n)=!isprime(n^2+n+41) && !issquare(n-40) \\ _Charles R Greathouse IV_, Sep 14 2014
%Y A055390 Cf. A007634 (numbers where n^2 + n + 41 is composite). A194634 (numbers in A007634 that are not in 3 parabolas). - _Matt C. Anderson_, Sep 26 2011
%Y A055390 Cf. A201998.
%K A055390 nonn
%O A055390 1,1
%A A055390 _J. Lowell_, Oct 08 2000
%E A055390 More terms from _David Wasserman_, Mar 19 2002