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

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

Offset: 1

Author

J. Lowell, Oct 08 2000

Keywords

• nonn

Comments

Numbers n such that n^2 + n + 41 is composite and n - 40 is not a square. - Charles R Greathouse IV, Sep 14 2014

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. A201998.

Programs

Maple

A007634 := {}:
for n from 0 to 1000 do
k := n^2+n+41:
if isprime(k) = false then A007634 := union(A007634, {n}) end if:
end do:
pv1 := Vector(1000, j -> (j-1)^2+40):
p1 := convert(pv1, set):
A055390 := minus(A007634, p1); # Matt C. Anderson, Sep 26 2011
remove(t -> issqr(t-40) or isprime(t^2+t+41), [$1..1000]); # Robert Israel, Nov 24 2017

Mathematica

Select[Range[260],CompositeQ[#^2+#+41]&&!IntegerQ[Sqrt[#-40]]&] (* Harvey P. Dale, Oct 20 2015 *)

PARI

is(n)=!isprime(n^2+n+41) && !issquare(n-40) \\ Charles R Greathouse IV, Sep 14 2014

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 14 2014

Extensions

More terms from David Wasserman, Mar 19 2002