A209247 a(n) = p(p(n)) + p(p( abs(n - p(p(n-1))) )), where p(n) = A188163(n) + 1 - [n=1].

1, 23, 33, 40, 61, 62, 65, 80, 115, 116, 117, 120, 125, 128, 141, 199, 228, 229, 230, 231, 234, 237, 238, 241, 246, 249, 264, 286, 289, 304, 370, 403, 449, 450, 451, 452, 453, 456, 459, 460, 461, 464, 469, 470, 473, 483, 486, 496, 518, 519, 522, 527, 530, 543

Offset: 2

Author

Roger L. Bagula, Jan 13 2013

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A087873, A188163.

Programs

Magma

nmax:=200;
h:=[n le 2 select 1 else Self(Self(n-1)) + Self(n - Self(n-1)): n in [1..10*nmax]]; // h = A004001
A188163:= function(n)
   for j in [1..8*nmax+1] do
       if h[j] eq n then return j; end if;
   end for;
end function;
// define a sequence based on A188163
p:= func< n | A188163(n) + 1 - 0^(n-1) >;
A209247:= function(n)
   if n le 2 then return 1;
   else return p(p(n)) + p(p(Abs(n - p(p(n-1)))));
   end if;
end function;
[A209247(n): n in [2..nmax]]; // G. C. Greubel, May 20 2024

Mathematica

nmax := 200;
h[n_]:= h[n]= If[n<3, 1, h[h[n-1]] + h[n-h[n-1]]]; (* A004001 *)
A188163[n_]:= For[m=1, True, m++, If[h[m]==n, Return[m]]];
(* define a sequence from A188163 *)
p[n_]:= A188163[n] + 1 - Boole[n==1];
a[n_]:= a[n]= If[n<3, 1, p[p[n]] + p[p[Abs[n-p[p[n-1]]]]]];
Table[a[n], {n, 2, nmax}]

SageMath

@CachedFunction
def h(n): return 1 if (n<3) else h(h(n-1)) + h(n - h(n-1)) # h=A004001
def A188163(n):
    for j in range(1,2*n+1):
        if h(j)==n: return j
# define a function based on A188163
def p(n): return A188163(n) + 1 - int(n==1)
@CachedFunction
def A209247(n): return 1 if (n<3) else p(p(n)) + p(p(abs(n - p(p(n-1)))))
[A209247(n) for n in range(2,201)] # G. C. Greubel, May 20 2024

Extensions

Edited by G. C. Greubel, Apr 23 2024