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

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, 33, 4, 191, 19, 290, 85, 672, 1, 11, 2, 383, 23, 362, 145, 17, 336, 8, 56, 1, 767, 29, 530, 181, 29, 222, 168, 4, 28, 4, 1535, 31, 842, 265, 3440, 494, 111, 84, 2, 14, 2, 3071

Offset

1,1

Comments

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.

Links

Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150, flattened).

Example

Array begins:
  [ 1]   2,   5,  11,    23,   47,   95, 191, 383,  767, ... = A153893
  [ 2]   3,  10,   5,    16,    8,    4,   2,   1,    4, ... = A033478
  [ 3]   5,  26,  13,    66,   33,   11,  56,  28,   14, ... = A057688
  [ 4]   7,  50,  25,     5,    1,    8,   4,   2,    1, ... = A368113
  [ 5]  11, 122,  61,   672,  336,  168,  84,  42,   21, ... = A368114
  [ 6]  13, 170,  85,    17,  222,  111,  37, 482,  241, ... = A057684
  [ 7]  17, 290, 145,    29,  494,  247,  19, 324,  162, ... = A368115
  [ 8]  19, 362, 181,  3440, 1720,  860, 430, 215,   43, ... = A057685
  [ 9]  23, 530, 265,    53, 1220,  610, 305,  61, 1404, ... = A057686
  [10]  29, 842, 421, 12210, 6105, 2035, 407,  37, 1074, ... = A057687
  ...    |    |    |
      A000040 | A066885 (from n = 2)
           A066872

Mathematica

Px1[p_, n_]:=Catch[For[i=1, i<PrimePi[p], i++, If[Divisible[n, Prime[i]], Throw[n/Prime[i]]]]; p*n+1];
A368085list[dmax_]:=With[{a=Reverse[Table[NestList[Px1[Prime[n], #]&, Prime[n], dmax-n], {n, dmax}]]}, Array[Diagonal[a, #]&, dmax, 1-dmax]];
A368085list[15] (* Generates 15 antidiagonals *)

Crossrefs

Rows 1-10: A153893, A033478, A057688, A368113, A368114, A057684, A368115, A057685, A057686, A057687.

Columns 1-3: A000040, A066872, A066885 (from n = 2).

Main diagonal gives A368159.

Cf. A057689, A057690, A057691.

Sequence in context: A265562 A140312 A088887 * A265546 A066911 A326229

Adjacent sequences: A368082 A368083 A368084 * A368086 A368087 A368088

Keyword

nonn,tabl,easy

Author

Paolo Xausa, Dec 11 2023

Status

approved