cp's OEIS Frontend

A368085 Square array read by ascending antidiagonals: row n is the trajectory of P under the 'Px+1' map, where P = n-th prime.

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