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A140491
Trajectory of 2 under repeated application of the map: n -> n + third-smallest number that does not divide n.
5
2, 7, 11, 15, 21, 26, 31, 35, 39, 44, 50, 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
1,1
LINKS
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 > 13.
G.f.: x*(4*x^12 + 6*x^11 + 6*x^10 + 5*x^9 + 4*x^8 + 4*x^7 + 5*x^6 + 5*x^5 + 6*x^4 + 4*x^3 + 4*x^2 + 5*x + 2)/(x^13 - x^12 - x + 1). (End)
MATHEMATICA
NestList[Complement[Range[3+#], Divisors[#]][[3]]+#&, 2, 60] (* Harvey P. Dale, Jan 15 2024 *)
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);
lista2(nn) = {a = 2; 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, A140492, A140493, A140494 (third-smallest sequences).
Sequence in context: A184485 A001960 A174008 * A122823 A063289 A287726
KEYWORD
nonn,changed
AUTHOR
Jacques Tramu, Jun 25 2008
EXTENSIONS
More terms from Michel Marcus, Oct 04 2018
STATUS
approved