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A140491 Trajectory of 2 under repeated application of the map: n -> n + third-smallest number that does not divide n.

%I A140491 #19 Nov 15 2024 09:04:17
%S A140491 2,7,11,15,21,26,31,35,39,44,50,56,62,67,71,75,81,86,91,95,99,104,110,
%T A140491 116,122,127,131,135,141,146,151,155,159,164,170,176,182,187,191,195,
%U A140491 201,206,211,215,219,224,230,236,242,247,251,255,261,266,271,275,279,284,290,296
%N A140491 Trajectory of 2 under repeated application of the map: n -> n + third-smallest number that does not divide n.
%H A140491 Harvey P. Dale, <a href="/A140491/b140491.txt">Table of n, a(n) for n = 1..1000</a>
%H A140491 <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 A140491 From _Chai Wah Wu_, Nov 14 2024: (Start)
%F A140491 A140490-A140493 all converge to the same trajectory.
%F A140491 a(n) = a(n-1) + a(n-12) - a(n-13) for n > 13.
%F A140491 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)
%t A140491 NestList[Complement[Range[3+#],Divisors[#]][[3]]+#&,2,60] (* _Harvey P. Dale_, Jan 15 2024 *)
%o A140491 (PARI) third(n) = {my(nb = 0, k = 1); while (nb != 3, if (n % k, nb++); if (nb != 3, k++);); k;}
%o A140491 f(n) = n + third(n);
%o A140491 lista2(nn) = {a = 2; print1(a, ", "); for (n=2, nn, newa = f(a); print1(newa, ", "); a = f(a););} \\ _Michel Marcus_, Oct 04 2018
%Y A140491 Cf. A140485, A140486, A140487, A140488, A140489 (second-smallest sequences).
%Y A140491 Cf. A140490, A140492, A140493, A140494 (third-smallest sequences).
%K A140491 nonn
%O A140491 1,1
%A A140491 _Jacques Tramu_, Jun 25 2008
%E A140491 More terms from _Michel Marcus_, Oct 04 2018