A145292 - OEIS

%I #25 May 12 2025 06:43:57

%S 1681,1763,2021,2491,3233,4331,5893,6683,6847,7181,7697,8051,8413,

%T 9353,10547,10961,12031,13847,14803,15047,15293,16043,16297,17071,

%U 18673,19223,19781,20633,21797,24221,25481,26123,26447,26773,27101,29111

%N Composite numbers generated by the Euler polynomial x^2 + x + 41.

%C The Euler polynomial x^2 + x + 41 gives primes for consecutive x from 0 to 39.

%C For numbers x for which x^2 + x + 41 is not prime see A007634.

%C Let P(x)=x^2 + x + 41. In view of identity P(x+P(x))=P(x)*P(x+1), all values of P(x+P(x)) are in the sequence. - _Vladimir Shevelev_, Jul 16 2012

%H Reinhard Zumkeller, <a href="/A145292/b145292.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n^2. [_Charles R Greathouse IV_, Dec 08 2011]

%t a = {}; Do[If[PrimeQ[x^2 + x + 41], null,AppendTo[a, x^2 + x + 41]], {x, 0, 500}]; a

%t Select[Table[x^2+x+41,{x,200}],CompositeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 21 2018 *)

%o (Haskell)

%o a145292 n = a145292_list !! (n-1)

%o a145292_list = filter ((== 0) . a010051) a202018_list

%o -- _Reinhard Zumkeller_, Dec 09 2011

%o (PARI) for(n=1,1e3,if(!isprime(t=n^2+n+41),print1(t", "))) \\ _Charles R Greathouse IV_, Dec 08 2011

%Y Cf. A005846, A007634, A145293, A145294.

%Y Intersection of A002808 and A202018; A010051.

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 06 2008