|
%I #19 Jul 20 2020 12:03:06
%S 1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,31,32,33,34,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,51,
%U 52,53,55,56,57,58,59,61,62,63,64,65,67,68,69,70,71,72,73,74,75,76,77,79
%N Numbers n such that zero is eventually reached when the map x -> A034460(x) is iterated, starting from x = n.
%C Numbers n for which A318880(n) = 0. - _Antti Karttunen_, Sep 23 2018
%C The sequence doesn't contain any numbers from attractor sets like A002827, A063991, A097024, A097030, etc, nor any number x such that the iteration of the map x -> A034460(x) would lead to such an attractor set (e.g., numbers in A097034 - A097037). - _Antti Karttunen_, Sep 24 2018, after the original author's example.
%H Antti Karttunen, <a href="/A097010/b097010.txt">Table of n, a(n) for n = 1..10001</a>
%t di[x_] :=Divisors[x];ta={{0}}; ud[x_] :=Part[di[x],Flatten[Position[GCD[di[x],Reverse[di[x]]],1]]]; asu[x_] :=Apply[Plus,ud[x]]-x;nsf[x_,ho_] :=NestList[asu,x,ho] Do[g=n;s=Last[NestList[asu,n,100]];If[Equal[s,0],Print[{n,s}]; ta=Append[ta,n]],{n,1,256}];ta = Delete[ta,1]
%o (PARI)
%o up_to = 10000;
%o A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
%o A318880(n) = { my(visited = Map()); for(j=1, oo, if(mapisdefined(visited, n), return(1), mapput(visited, n, j)); n = A034460(n); if(!n,return(0))); };
%o A097010list(up_to) = { my(v = vector(up_to), k=0, n=1); while(k<up_to,if(!A318880(n), k++; v[k] = n); n++); (v); };
%o v097010 = A097010list(up_to);
%o A097010(n) = v097010[n]; \\ _Antti Karttunen_, Sep 24 2018
%Y Cf. A002827, A034460, A063991, A097024, A097030, A097031, A097032, A097033, A097034, A097035, A097036, A097037.
%Y Cf. A003062 (complement), A318880.
%Y Differs from A129487 for the first time at n=51, as A129487(51) = 54, but that term is lacking here, as in this sequence a(51) = 55.
%K nonn
%O 1,2
%A _Labos Elemer_, Aug 31 2004
%E Edited by _Antti Karttunen_, Sep 24 2018
|
