A172262 a(n) is the greatest root of the Laguerre polynomial L_n(x) to the nearest integer

1, 3, 6, 9, 13, 16, 19, 23, 26, 30, 33, 37, 41, 44, 48, 52, 55, 59, 63, 67, 70, 74, 78, 81, 85, 89, 93, 97, 100, 104, 108, 112, 116, 119, 123, 127, 131, 135, 138, 142, 146, 150, 154, 158, 161, 165, 169, 173, 177, 181, 185, 188, 192, 196, 200, 204, 208, 212, 215, 219, 223, 227

Offset

1,2

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.

Links

Table of n, a(n) for n=1..62.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Maple

for p from 1 to 10 do; a:=round(evalf(realroot(expand(LaguerreL(p, 0, x)), 1/10000))[-1][1]):printf(`%d, `, a): od: # Michel Lagneau, Mar 11 2023

Mathematica

a[n_] := Round@  Max[x /. Solve[LaguerreL[n, x] == 0, x]]; Array[a, 60] (* Amiram Eldar, Mar 11 2023 *)

Prog

(PARI) a(n) = round(vecmax(polrootsreal(pollaguerre(n)))); \\ Michel Marcus, Mar 10 2023

Crossrefs

Sequence in context: A080081 A171982 A066343 * A184909 A289037 A060605

Adjacent sequences: A172259 A172260 A172261 * A172263 A172264 A172265

Keyword

nonn

Author

Michel Lagneau, Jan 30 2010

Extensions

Corrected by Michel Marcus, Mar 10 2023

Status

approved