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

%I A140493 #17 Nov 15 2024 09:04:06
%S A140493 4,10,16,22,27,32,38,43,47,51,56,62,67,71,75,81,86,91,95,99,104,110,
%T A140493 116,122,127,131,135,141,146,151,155,159,164,170,176,182,187,191,195,
%U A140493 201,206,211,215,219,224,230,236,242,247,251,255,261,266,271,275,279,284,290,296
%N A140493 Trajectory of 4 under repeated application of the map: n -> n + third-smallest number that does not divide n.
%H A140493 Harvey P. Dale, <a href="/A140493/b140493.txt">Table of n, a(n) for n = 1..1000</a>
%H A140493 <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 A140493 From _Chai Wah Wu_, Nov 14 2024: (Start)
%F A140493 A140490-A140493 all converge to the same trajectory.
%F A140493 a(n) = a(n-1) + a(n-12) - a(n-13) for n > 23.
%F A140493 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)
%t A140493 NestList[Complement[Range[#+10],Divisors[#]][[3]]+#&,4,60] (* _Harvey P. Dale_, Aug 28 2023 *)
%o A140493 (PARI) third(n) = {my(nb = 0, k = 1); while (nb != 3, if (n % k, nb++); if (nb != 3, k++);); k;}
%o A140493 f(n) = n + third(n);
%o A140493 lista4(nn) = {a = 4; print1(a, ", "); for (n=2, nn, newa = f(a); print1(newa, ", "); a = f(a););} \\ _Michel Marcus_, Oct 04 2018
%Y A140493 Cf. A140485, A140486, A140487, A140488, A140489 (second-smallest sequences).
%Y A140493 Cf. A140491, A140492, A140493, A140494 (third-smallest sequences).
%K A140493 nonn
%O A140493 1,1
%A A140493 _Jacques Tramu_, Jun 25 2008
%E A140493 More terms from _Michel Marcus_, Oct 04 2018