OFFSET
1,1
COMMENTS
The old definition was "Least numbers not generated by Eisenstein's algorithm: m=1 n=1, then insert between them m+n, at stage p=1. (E.g. next stage (p=2) of Eisenstein's algorithm would be m, m+m+n, m+n, m+n+n, n). The maximum of these symmetric row elements at stage p is fibonacci(p+2); but how to determine the first number not generated at stage p?"
LINKS
Don Reble, C++ program for A135510 and A293160
G. Eisenstein, Über ein einfaches Mittel zur Auffindung der höheren Reciprocitätsgesetze und der mit ihnen zu verbindenden Ergänzungssätze, Journal für die reine und angewandte Mathematik, Volume 39 (1850), page 351ff.
M. A. Stern, Über eine zahlentheoretische Funktion, J. Reine Angew. Math., 55 (1858), 193-220.
MAPLE
A049456 := proc(n, k)
option remember;
if n =1 then
if k >= 0 and k <=1 then
1;
else
0 ;
end if;
elif type(k, 'even') then
procname(n-1, k/2) ;
else
procname(n-1, (k+1)/2)+procname(n-1, (k-1)/2) ;
end if;
end proc: # R. J. Mathar, Dec 12 2014
mex := proc(L)
local k;
for k from 1 do
if not k in L then
return k;
end if;
end do:
end proc:
rho:=n->[seq(A049456(n, k), k=0..2^(n-1))];
[seq(mex(rho(n)), n=1..16)]; # N. J. A. Sloane, Oct 14 2017
MATHEMATICA
(* T is A049456 *)
T[n_, k_] := T[n, k] = If[n == 1, If[k >= 0 && k <= 1, 1, 0], If[EvenQ[k], T[n-1, k/2], T[n-1, (k+1)/2] + T[n-1, (k-1)/2]]];
mex[L_] := Module[{k}, For[k = 1, True, k++, If[FreeQ[L, k], Return[k]]]];
rho[n_] := Table[T[n, k], {k, 0, 2^(n-1)}];
a[n_] := a[n] = mex[rho[n]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Aug 03 2023, after Maple code *)
CROSSREFS
KEYWORD
nonn
AUTHOR
mc (da-da(AT)lycos.de), Feb 09 2008
EXTENSIONS
Entry revised by N. J. A. Sloane, Oct 14 2017
a(29)-a(39) from Don Reble, Oct 16 2016
STATUS
approved