A330139 - OEIS

%I #29 Sep 08 2023 22:37:08

%S 1,1,2,3,1,4,5,9,14,23,37,5,42,47,89,136,225,361,586,947,73,1020,1093,

%T 2113,3206,5319,8525,13844,22369,36213,58582,94795,153377,248172,

%U 401549,649721,1051270,1700991,2752261,4453252,7205513,11658765,18864278,30523043,49387321,79910364,129297685,209208049,338505734,547713783

%N 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).

%H Alois P. Heinz, <a href="/A330139/b330139.txt">Table of n, a(n) for n = 1..4800</a>

%F 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).

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

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

%p a:= proc(n) option remember; `if`(n<2, n, (t->

%p       `if`(irem(t, n)=0, t/n, t))(a(n-1)+a(n-2)))

%p     end:

%p seq(a(n), n=1..50);  # _Alois P. Heinz_, Mar 28 2020

%t 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 *)

%t 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 *)

%o (Pascal)

%o Begin

%o .....n1[1]:=1;

%o .....n1[2]:=1;

%o .....writeln(n1[1],',');

%o .....writeln(n1[2],',');

%o .....for n2:=3 to 100 do

%o .....begin

%o ........n1[n2] := n1[n2-1]+n1[n2-2];

%o ........if n1[n2]mod(n2) = 0 then

%o ........begin

%o ...........n1[n2] := int(n1[n2]/n2);

%o ........end;

%o ........writeln(n1[n2],',');

%o .....end;

%o End.

%Y Cf. A000045, A333578.

%K nonn,easy

%O 1,3

%A _Eder Vanzei_, Dec 02 2019

%E Incorrect conjectured g.f. removed by _Alois P. Heinz_, Mar 28 2020