OFFSET

1,2

COMMENTS

1, 2 and the third column of A357554.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 3 if n is divisible by 3.

a(3*k+1) = k+1.

a(15*k+5) = 5 for k >= 1.

a(15*k+11) = 3*k+3.

a(255*k+137) = 15*k+9 for k >= 1.

EXAMPLE

a(4) = 2 because we have 3 -> floor(4/3) + (4 mod 3) = 2 -> floor(4/2) + (4 mod 2) = 2.

MAPLE

g:= proc(n, k) local x, S;

S:= {k};

x:= k;

do

x:= iquo(n, x) + irem(n, x);

if member(x, S) then return x fi;

S:= S union {x};

od

end proc:

seq(g(n, 3), n=1..100);

MATHEMATICA

T[n_, k_] := Module[{x, S}, S = {k}; x = k; While[True, x = Total@QuotientRemainder[n, x]; If[MemberQ[S, x], Return[x]]; S = S~Union~{x}]];

a[n_] := T[n, 3];

Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 17 2022, after Maple code *)

PROG

(Python)

def a(n):

seen, x = set(), 3

while x not in seen: seen.add(x); q, r = divmod(n, x); x = q + r

return x

print([a(n) for n in range(1, 90)]) # Michael S. Branicky, Oct 06 2022~

CROSSREFS

KEYWORD

nonn,look

AUTHOR

J. M. Bergot and Robert Israel, Oct 06 2022

STATUS

approved