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A368159 The n-th term in the trajectory of the n-th prime P under the 'Px+1' map.

%I A368159 #15 Dec 14 2023 04:20:38
%S A368159 2,10,13,5,336,111,19,215,1404,537,318,19,1,1,12,19,1,41231,103,18,1,
%T A368159 10,42,3120474,32580,17,26,351348,260402,38082,128,60457,138,140,
%U A368159 547278,6869,1,164,21,87,90,16245,12,194,33,90645,106,224,1,230,1,60,121,1
%N A368159 The n-th term in the trajectory of the n-th prime P under the 'Px+1' map.
%C A368159 See A057684 for definition.
%H A368159 Paolo Xausa, <a href="/A368159/b368159.txt">Table of n, a(n) for n = 1..1000</a>
%F A368159 a(n) = A368085(n,n).
%e A368159 For n= 4: prime(4)  =  7 ->   50 ->  25 ->   5  = a(4).
%e A368159 For n= 5: prime(5)  = 11 ->  122 ->  61 -> 672 -> 336  = a(5).
%e A368159 For n= 6: prime(6)  = 13 ->  170 ->  85 ->  17 -> 222 -> 111  = a(6).
%e A368159 For n=13: prime(13) = 41 -> 1682 -> 841 ->  29 ->   1 ->  42 ->
%e A368159                       21 ->    7 ->   1 ->  42 ->  21 ->   7 -> 1 = a(13).
%t A368159 Px1[p_, n_]:=Catch[For[i=1, i<PrimePi[p], i++, If[Divisible[n, Prime[i]], Throw[n/Prime[i]]]]; p*n+1];
%t A368159 A368159[n_]:=Nest[Px1[Prime[n], #]&, Prime[n],n-1];
%t A368159 Array[A368159,100] (* _Paolo Xausa_, Dec 14 2023 *)
%Y A368159 Main diagonal of A368085.
%Y A368159 Cf. A000040, A057684, A057689, A057690, A057691.
%K A368159 nonn
%O A368159 1,1
%A A368159 _Alois P. Heinz_, Dec 13 2023