1,1

Euler polynomial is giving primes for consecutive x from 0 to 39.

Numbers x for which x^2 + x + 41 is not prime see A007634.

Composite numbers of the form x^2 + x + 41 see A145292.

a(1)=40 because when x=40 than x^2+x+41=1681=41*41 (1 distinct prime divisor)

a(2)=41 because when x=41 than x^2+x+41=1763=41*43 (2 distinct prime divisors)

a(3)=420 because when x=420 than x^2+x+41=176861=47*53*71 (3 distinct prime divisors)

a(4)=2911 because when x=2911 than x^2+x+41=8476873=41*47*53*83 (4 distinct prime divisors)

a(5)=38913 because when x=38913 than x^2+x+41=1514260523=43*47*61*71*173 (5 distinct prime divisors)

a(6)=707864 because when x=707864 than x^2+x+41=501072150401=41*43*47*53*71*1607 (6 distinct prime divisors)

a(7)=6618260 because when x=6618260 than x^2+x+41=43801372045901=41*43*47*61*83*131*797 (7 distinct prime divisors)

a = {}; Do[x = 1; While[Length[FactorInteger[x^2 + x + 41]] < k - 1, x++ ]; AppendTo[a, x]; Print[x], {k, 2, 10}]; a (*Artur Jasinski*)

A005846, A007634, A145292, A145294, A145295

Sequence in context: A082763 A007634 A128843 this_sequence A111167 A070980 A118473

Adjacent sequences: A145290 A145291 A145292 this_sequence A145294 A145295 A145296

nonn

Artur Jasinski (grafix(AT)csl.pl), Oct 07 2008