A140488 Trajectory of 5 under repeated application of the map: n -> n + second-smallest number that does not divide n.

5, 8, 13, 16, 21, 25, 28, 33, 37, 40, 46, 50, 54, 59, 62, 66, 71, 74, 78, 83, 86, 90, 97, 100, 106, 110, 114, 119, 122, 126, 131, 134, 138, 143, 146, 150, 157, 160, 166, 170, 174, 179, 182, 186, 191, 194, 198, 203, 206, 210, 218, 222, 227, 230, 234, 239, 242, 246

Offset: 1

Author

Eric Angelini, Jun 25 2008

Keywords

• nonn

Links

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

Crossrefs

Cf. A140485, A140486, A140487, A140489.

Programs

Maple

f:= proc(n) local k,c;
c:= 0:
for k from 2 do
  if n mod k <> 0 then
    if c = 1 then return n+k fi;
    c:= 1;
  fi
od
end proc:
R:= 5: t:= 5:
for count from 2 to 100 do
  t:= f(t);
  R:= R,t;
od:
R; # Robert Israel, Oct 19 2021

Mathematica

a = {5}; Do[AppendTo[a, a[[ -1]] + Select[Range[a[[ -1]]], Mod[a[[ -1]], # ] > 0 &][[2]]], {60}]; a (* Stefan Steinerberger, Jul 01 2008 *)

Python

def aupton(terms):
    alst = [5]
    while len(alst) < terms:
        an, k, smallest = alst[-1], 2, False
        while not smallest or an%k == 0:
            if not smallest and an%k != 0: smallest = True
            k += 1
        alst.append(an+k)
    return alst
print(aupton(58)) # Michael S. Branicky, Oct 19 2021

Formula

It appears that a(n+98) = a(n)+420 for n >= 9. - Robert Israel, Oct 19 2021

Extensions

Corrected and extended by Stefan Steinerberger, Jul 01 2008