A140490 Trajectory of 1 under repeated application of the map: n -> n + third-smallest number that does not divide n.

1, 5, 9, 14, 19, 23, 27, 32, 38, 43, 47, 51, 56, 62, 67, 71, 75, 81, 86, 91, 95, 99, 104, 110, 116, 122, 127, 131, 135, 141, 146, 151, 155, 159, 164, 170, 176, 182, 187, 191, 195, 201, 206, 211, 215, 219, 224, 230, 236, 242, 247, 251, 255, 261, 266, 271, 275, 279, 284, 290, 296

Offset

1,2

Comments

Suggested by Eric Angelini.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

a(n+12) = a(n) + 60 for n >= 13. - Robert Israel, Jan 17 2023

From Chai Wah Wu, Nov 14 2024: (Start)

A140490-A140493 all converge to the same trajectory.

a(n) = a(n-1) + a(n-12) - a(n-13) for n > 25.

G.f.: x*(x^24 + 2*x^23 + x^22 - x^21 - 2*x^20 + x^18 + 2*x^17 - x^16 - x^15 + x^14 + 2*x^13 + 4*x^12 + 4*x^11 + 4*x^10 + 5*x^9 + 6*x^8 + 5*x^7 + 4*x^6 + 4*x^5 + 5*x^4 + 5*x^3 + 4*x^2 + 4*x + 1)/(x^13 - x^12 - x + 1). (End)

Maple

f:= proc(n) local k, count;
  count:= 0;
  for k from 2 do
    if n mod k <> 0 then count:= count+1; if count = 3 then return n+k fi fi
  od
end proc:
R:= 1: x:= 1:
for i from 1 to 100 do x:= f(x); R:= R, x od:
R; # Robert Israel, Jan 17 2023

Mathematica

NestList[#+Complement[Range[#+50], Divisors[#]][[3]]&, 1, 60] (* Harvey P. Dale, Apr 21 2022 *)

Prog

(PARI) third(n) = {my(nb = 0, k = 1); while (nb != 3, if (n % k, nb++); if (nb != 3, k++); ); k; }
f(n) = n + third(n);
lista1(nn) = {a = 1; print1(a, ", "); for (n=2, nn, newa = f(a); print1(newa, ", "); a = f(a); ); } \\ Michel Marcus, Oct 04 2018

Crossrefs

Cf. A140485, A140486, A140487, A140488, A140489 (second-smallest sequences).

Cf. A140491, A140492, A140493, A140494 (third-smallest sequences).

Sequence in context: A314884 A314885 A314886 * A314887 A316324 A247972

Adjacent sequences: A140487 A140488 A140489 * A140491 A140492 A140493

Keyword

nonn

Author

Jacques Tramu, Jun 25 2008

Extensions

More terms from Michel Marcus, Oct 04 2018

Status

approved