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

1,1

Links

Table of n, a(n) for n=1..56.

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

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)

Mathematica

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

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);
lista3(nn) = {a = 3; 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. A140490, A140491, A140493, A140494 (third-smallest sequences).

Sequence in context: A104656 A179993 A252658 * A184517 A028252 A299647

Adjacent sequences: A140489 A140490 A140491 * A140493 A140494 A140495

Keyword

nonn,changed

Author

Jacques Tramu, Jun 25 2008

Extensions

More terms from Harvey P. Dale, Apr 04 2015

Status

approved