A174305
Values of the family of polynomials y = x^n + 1 at point x = discriminant of y.
Original entry on oeis.org
2, 17, -19682, 4294967297, 298023223876953126, 10314424798490535546171949057, -256923577521058878088611477224235621321606, 6277101735386680763835789423207666416102355444464034512897, 196627050475552913618075908526912116283103450944214766927315415537966391196810
Offset: 1
-
f:= proc(n) local x, d,p;
p:= x^n+1;
eval(p,x=discrim(p,x))
end proc:
map(f, [$1..10]); # Robert Israel, Jan 03 2020
-
Clear[x]; s = {}; Do[d = Discriminant[x^n + 1, x]; AppendTo[s, d^n - 1], {n, 1, 10}]; s
-
a(n) = my(p=x^n+1); subst(p, x, poldisc(p)); \\ Michel Marcus, Mar 02 2023
A174308
Values of the family of polynomials y = Sum_{z = 0..n-1} x^z at point x = discriminant of y.
Original entry on oeis.org
1, 2, 7, -3855, 246109501, 3658981728433681, 22537999301860113141522943, -85070267212918892756053780436965654527, 273892802259521776518514883585359984420603636167980521, 1000000010000000100000001000000010000000100000001000000010000000100000001
Offset: 1
-
Clear[x]; s = {}; Do[pol = Simplify[(x^n - 1)/(x - 1)]; d = Discriminant[pol, x]; AppendTo[s, pol /. x -> d], {n, 1, 10}]; s
-
a(n) = my(p=sum(k=0, n-1, x^k)); subst(p, x, poldisc(p)); \\ Michel Marcus, Mar 02 2023
A174311
Value of the n-th cyclotomic polynomial at the discriminant of that polynomial.
Original entry on oeis.org
0, 2, 7, 17, 246109501, 13, 22537999301860113141522943, 4294967297, 58149737003032434092905183, 242203001, 5313022609595033985218523349395070147785700752531778166637386100465086995951866123901089470951
Offset: 1
C_4(x) = x^2 + 1 has discriminant -4 so a(4) = C_4(-4) = 17. - _Robert Israel_, Jul 19 2016
-
seq(numtheory:-cyclotomic(n, discrim(numtheory:-cyclotomic(n,x),x)), n=1..20); # Robert Israel, Jul 19 2016
-
s = {}; Do[d = Discriminant[Cyclotomic[n, x], x]; AppendTo[s, Cyclotomic[n, d]], {n, 1, 20}]; s
A174306
Values of the family of polynomials y = x^n - x - 1 at point x = discriminant of y.
Original entry on oeis.org
-1, 19, -12145, 6414248203, 194380520729322479, 15218845171211140441021214899, -170806730553626811832652589499918854529297, 9209820606607584866627264481712305648950696250051751911479, 132009474006996885142958525887127779016665316066680074875830065810704441797439
Offset: 1
-
Clear[x]; s = {}; Do[d = Discriminant[x^n - x - 1, x]; AppendTo[s, d^n - d - 1], {n, 1, 10}]; s
-
a(n) = my(p=x^n-x-1); subst(p, x, poldisc(p)); \\ Michel Marcus, Mar 02 2023
A174307
Values of the family of polynomials y = x^n + x + 1 at point x = discriminant of y.
Original entry on oeis.org
3, 7, -29821, 2750058711, 441800144752584283, 6804431770345241082279621151, -377859250831193351209596088271916078121597, 4196483202812521725112100379233057161478356010053715361355, 287968238412833577612998830601797972725819919777961202447931475131073570213331
Offset: 1
-
Clear[x]; s = {}; Do[d = Discriminant[x^n + x + 1, x]; AppendTo[s, d^n + d + 1], {n, 1, 10}]; s
-
a(n) = my(p=x^n+x+1); subst(p, x, poldisc(p)); \\ Michel Marcus, Mar 02 2023
A174309
Value of the polynomial y = (x^(2n-1) + 1)/(x + 1) at the point x = discriminant of y.
Original entry on oeis.org
1, 13, 242203001, 22540681439108936194378057, 273892687731183836066546120028455556686378073137630689
Offset: 1
-
s = {}; Do[pol = Simplify[(x^n + 1)/(x + 1)]; d = Discriminant[pol, x]; AppendTo[s, pol /. x -> d], {n, 1, 10, 2}]; s
-
a(n) = my(p=(x^(2*n-1) + 1)/(x + 1)); subst(p, x, poldisc(p)); \\ Michel Marcus, Mar 02 2023
A174310
Values of the family of polynomials y = (x^(n+1) + 1)/(x + 1) at point x = discriminant of y.
Original entry on oeis.org
1, 0, 13, -4369, 242203001, 3653339505259535, 22540681439108936194378057, -85070916250026219054240312625736187905, 273892687731183836066546120028455556686378073137630689
Offset: 1
-
s = {}; Do[k = PolynomialQuotient[(x^n + 1), (x + 1), x]; d = Discriminant[k, x]; AppendTo[s, k /. x -> d], {n, 1, 10}]; s
Showing 1-7 of 7 results.
Comments