A330139 a(1)=1 and a(2)=1; if a(n-1) + a(n-2) == 0 (mod n) then a(n) = (a(n-1) + a(n-2))/n else a(n) = a(n-1) + a(n-2).

1, 1, 2, 3, 1, 4, 5, 9, 14, 23, 37, 5, 42, 47, 89, 136, 225, 361, 586, 947, 73, 1020, 1093, 2113, 3206, 5319, 8525, 13844, 22369, 36213, 58582, 94795, 153377, 248172, 401549, 649721, 1051270, 1700991, 2752261, 4453252, 7205513, 11658765, 18864278, 30523043, 49387321, 79910364, 129297685, 209208049, 338505734, 547713783

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..4800

Formula

If a(n-1) + a(n-2) == 0 (mod n) then a(n) = (a(n-1) + a(n-2))/n, otherwise a(n) = a(n-1) + a(n-2).

a(n) != a(n-1) + a(n-2) for n in A333578.

Example

a(5) = 1 because a(4) + a(3) = 5, and 5 mod 5 = 0, so a(5) = (a(4) + a(3))/5 = 1.

Maple

a:= proc(n) option remember; `if`(n<2, n, (t->
      `if`(irem(t, n)=0, t/n, t))(a(n-1)+a(n-2)))
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Mar 28 2020

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = If[Divisible[(s = a[n-1] + a[n-2]), n], s/n, s]; Array[a, 50] (* Amiram Eldar, Dec 02 2019 *)
nxt[{n_, a_, b_}]:={n+1, b, Which[Divisible[a+b, n+1], (a+b)/(n+1), True, a+b]}; NestList[nxt, {2, 1, 1}, 50][[All, 2]] (* Harvey P. Dale, May 22 2021 *)

Prog

(Pascal)
Begin
.....n1[1]:=1;
.....n1[2]:=1;
.....writeln(n1[1], ', ');
.....writeln(n1[2], ', ');
.....for n2:=3 to 100 do
.....begin
........n1[n2] := n1[n2-1]+n1[n2-2];
........if n1[n2]mod(n2) = 0 then
........begin
...........n1[n2] := int(n1[n2]/n2);
........end;
........writeln(n1[n2], ', ');
.....end;
End.

Crossrefs

Cf. A000045, A333578.

Sequence in context: A338240 A265755 A341130 * A349358 A046671 A178760

Adjacent sequences: A330136 A330137 A330138 * A330140 A330141 A330142

Keyword

nonn,easy

Author

Eder Vanzei, Dec 02 2019

Extensions

Incorrect conjectured g.f. removed by Alois P. Heinz, Mar 28 2020

Status

approved