A172262 - OEIS

%I #17 Mar 13 2023 13:29:49

%S 1,3,6,9,13,16,19,23,26,30,33,37,41,44,48,52,55,59,63,67,70,74,78,81,

%T 85,89,93,97,100,104,108,112,116,119,123,127,131,135,138,142,146,150,

%U 154,158,161,165,169,173,177,181,185,188,192,196,200,204,208,212,215,219,223,227

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

%D 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.

%H M. Abramowitz and I. A. Stegun, eds.,<a href="http://apps.nrbook.com/abramowitz_and_stegun/index.html"> Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>

%p 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

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

%o (PARI) a(n) = round(vecmax(polrootsreal(pollaguerre(n)))); \\ _Michel Marcus_, Mar 10 2023

%K nonn

%O 1,2

%A _Michel Lagneau_, Jan 30 2010

%E Corrected by _Michel Marcus_, Mar 10 2023