A145294 Smallest x >= 0 such that the Euler polynomial x^2 + x + 41 has a prime divisor of multiplicity n.

0, 40, 1721, 14144, 2294005, 326924482, 6386359423, 1341160319494, 149759650255065, 1167478867440605, 243422399538851918, 9662500171353620019, 122479951673184550424, 12148820281768361731597, 177497315692809432279207, 11767210525408975519141638

Offset

1,2

Comments

The Euler polynomial gives primes for consecutive x from 0 to 39.

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

For composite numbers of the form x^2 + x + 41, see A145292.

For the smallest x such that polynomial x^2 + x + 41 has exactly n distinct prime divisors, see A145293.

Sequence interpreted as a(n)^2 + a(n) + 41 having a prime divisor with multiplicity that is exactly n. - Bert Dobbelaere, Jan 22 2019

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..100

Bert Dobbelaere, Python program

Example

a(2)=40 because when x=40 then x^2 + x + 41 = 1681 = 41^2;
a(3)=1721 because when x=1721 then x^2 + x + 41 = 2963603 = 43*41^3;
a(4)=14144 because when x=14144 then x^2 + x + 41 = 200066921 = 41*47^4;
a(5)=2294005 because when x=2294005 then x^2 + x + 41 = 5262461234071 = 35797*43^5.
a(6)=326924482: a(6)^2 + a(6) + 41 = 106879617257892847 = 9915343 * 47^6. - Hugo Pfoertner, Mar 08 2018

Crossrefs

Cf. A005846, A007634, A145292, A145293, A145295.

Sequence in context: A229584 A140702 A223609 * A147520 A190926 A143314

Adjacent sequences: A145291 A145292 A145293 * A145295 A145296 A145297

Keyword

nonn

Author

Artur Jasinski, Oct 07 2008

Extensions

Title changed, a(1) and a(6) from Hugo Pfoertner, Mar 08 2018

More terms from Bert Dobbelaere, Jan 22 2019

Status

approved