A357610 Start with x = 3 and repeat the map x -> floor(n/x) + (n mod x) until an x occurs that has already appeared, then that is a(n).

1, 2, 3, 2, 3, 3, 3, 4, 3, 4, 3, 3, 5, 6, 3, 6, 5, 3, 7, 5, 3, 8, 7, 3, 9, 6, 3, 10, 9, 3, 11, 8, 3, 12, 5, 3, 13, 10, 3, 14, 9, 3, 15, 11, 3, 16, 11, 3, 17, 5, 3, 18, 5, 3, 19, 12, 3, 20, 11, 3, 21, 14, 3, 22, 5, 3, 23, 8, 3, 24, 15, 3, 25, 14, 3, 26, 17, 3, 27, 5, 3, 28, 11, 3, 29, 18, 3, 30, 9

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

Cf. A357554.

Sequence in context: A083060 A346643 A272979 * A102351 A078173 A248005

Adjacent sequences: A357607 A357608 A357609 * A357611 A357612 A357613

Keyword

nonn,look

Author

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

Status

approved