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%I #29 Dec 13 2023 19:00:12
%S 2,3,5,5,10,11,7,26,5,23,11,50,13,16,47,13,122,25,66,8,95,17,170,61,5,
%T 33,4,191,19,290,85,672,1,11,2,383,23,362,145,17,336,8,56,1,767,29,
%U 530,181,29,222,168,4,28,4,1535,31,842,265,3440,494,111,84,2,14,2,3071
%N Square array read by ascending antidiagonals: row n is the trajectory of P under the 'Px+1' map, where P = n-th prime.
%C The 'Px+1 map' is defined as follows: if there exists p = smallest prime < P which divides x then x = x/p, otherwise x = P*x + 1.
%H Paolo Xausa, <a href="/A368085/b368085.txt">Table of n, a(n) for n = 1..11325</a> (antidiagonals 1..150, flattened).
%e Array begins:
%e [ 1] 2, 5, 11, 23, 47, 95, 191, 383, 767, ... = A153893
%e [ 2] 3, 10, 5, 16, 8, 4, 2, 1, 4, ... = A033478
%e [ 3] 5, 26, 13, 66, 33, 11, 56, 28, 14, ... = A057688
%e [ 4] 7, 50, 25, 5, 1, 8, 4, 2, 1, ... = A368113
%e [ 5] 11, 122, 61, 672, 336, 168, 84, 42, 21, ... = A368114
%e [ 6] 13, 170, 85, 17, 222, 111, 37, 482, 241, ... = A057684
%e [ 7] 17, 290, 145, 29, 494, 247, 19, 324, 162, ... = A368115
%e [ 8] 19, 362, 181, 3440, 1720, 860, 430, 215, 43, ... = A057685
%e [ 9] 23, 530, 265, 53, 1220, 610, 305, 61, 1404, ... = A057686
%e [10] 29, 842, 421, 12210, 6105, 2035, 407, 37, 1074, ... = A057687
%e ... | | |
%e A000040 | A066885 (from n = 2)
%e A066872
%t Px1[p_,n_]:=Catch[For[i=1,i<PrimePi[p],i++,If[Divisible[n,Prime[i]],Throw[n/Prime[i]]]];p*n+1];
%t A368085list[dmax_]:=With[{a=Reverse[Table[NestList[Px1[Prime[n],#]&,Prime[n],dmax-n],{n,dmax}]]},Array[Diagonal[a,#]&,dmax,1-dmax]];
%t A368085list[15] (* Generates 15 antidiagonals *)
%Y Rows 1-10: A153893, A033478, A057688, A368113, A368114, A057684, A368115, A057685, A057686, A057687.
%Y Columns 1-3: A000040, A066872, A066885 (from n = 2).
%Y Main diagonal gives A368159.
%Y Cf. A057689, A057690, A057691.
%K nonn,tabl,easy
%O 1,1
%A _Paolo Xausa_, Dec 11 2023
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