A140493 Trajectory of 4 under repeated application of the map: n -> n + third-smallest number that does not divide n.

4, 10, 16, 22, 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

Author

Jacques Tramu, Jun 25 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

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

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

Programs

Mathematica

NestList[Complement[Range[#+10],Divisors[#]][[3]]+#&,4,60] (* Harvey P. Dale, Aug 28 2023 *)

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);
lista4(nn) = {a = 4; print1(a, ", "); for (n=2, nn, newa = f(a); print1(newa, ", "); a = f(a););} \\ Michel Marcus, Oct 04 2018

Formula

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 > 23.

G.f.: x*(x^22 + 2*x^21 + x^20 - x^19 - 2*x^18 - 2*x^14 - 2*x^13 + x^12 + 6*x^11 + 5*x^10 + 4*x^9 + 4*x^8 + 5*x^7 + 6*x^6 + 5*x^5 + 5*x^4 + 6*x^3 + 6*x^2 + 6*x + 4)/(x^13 - x^12 - x + 1). (End)

Extensions

More terms from Michel Marcus, Oct 04 2018