A140492 - OEIS

%I #12 Nov 15 2024 09:04:12

%S 3,8,14,19,23,27,32,38,43,47,51,56,62,67,71,75,81,86,91,95,99,104,110,

%T 116,122,127,131,135,141,146,151,155,159,164,170,176,182,187,191,195,

%U 201,206,211,215,219,224,230,236,242,247,251,255,261,266,271,275

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

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

%F From _Chai Wah Wu_, Nov 14 2024: (Start)

%F A140490-A140493 all converge to the same trajectory.

%F a(n) = a(n-1) + a(n-12) - a(n-13) for n > 24.

%F 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)

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

%o (PARI) third(n) = {my(nb = 0, k = 1); while (nb != 3, if (n % k, nb++); if (nb != 3, k++);); k;}

%o f(n) = n + third(n);

%o lista3(nn) = {a = 3; print1(a, ", "); for (n=2, nn, newa = f(a); print1(newa, ", "); a = f(a););} \\ _Michel Marcus_, Oct 04 2018

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

%Y Cf. A140490, A140491, A140493, A140494 (third-smallest sequences).

%K nonn,changed

%O 1,1

%A _Jacques Tramu_, Jun 25 2008

%E More terms from _Harvey P. Dale_, Apr 04 2015