A140492 Trajectory of 3 under repeated application of the map: n -> n + third-smallest number that does not divide n.

3, 8, 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

Offset: 1

Author

Jacques Tramu, Jun 25 2008

Keywords

• nonn

Links

• 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. A140490, A140491, A140493, A140494 (third-smallest sequences).

Programs

Mathematica

Join[{3},NestList[#+Complement[Range[#],Divisors[#]][[3]]&,8,50]] (* Harvey P. Dale, Apr 04 2015 *)

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);
lista3(nn) = {a = 3; 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 > 24.

G.f.: x*(x^23 + 2*x^22 + x^21 - x^20 - 2*x^19 + x^17 + 2*x^16 - x^15 - 2*x^14 + 3*x^12 + 5*x^11 + 4*x^10 + 4*x^9 + 5*x^8 + 6*x^7 + 5*x^6 + 4*x^5 + 4*x^4 + 5*x^3 + 6*x^2 + 5*x + 3)/(x^13 - x^12 - x + 1). (End)

Extensions

More terms from Harvey P. Dale, Apr 04 2015