A362813 Number of numbers that occur more than once in column n of McGarvey's array (A007062).

0, 2, 3, 4, 6, 6, 7, 9, 11, 12, 14, 13, 14, 16, 15, 17, 21, 20, 22, 25, 24, 25, 29, 26, 26, 31, 29, 31, 36, 33, 33, 40, 37, 36, 44, 41, 39, 48, 42, 44, 50, 44, 48, 53, 49, 49, 56, 54, 53, 62, 55, 56, 69, 61, 59, 66, 61, 66, 73, 65, 64, 75, 71, 70, 80, 72, 71

Offset: 1

Author

Clark Kimberling, May 04 2023

Keywords

• nonn

Examples

			Corner of McGarvey's array (from A007062):
   1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
   2  1  4  3  6  5  8  7 10  9 12 11 14 13 16 15 18 17 20 19
   4  1  2  5  6  3 10  7  8 11 12  9 16 13 14 17 18 15 22 19
   5  2  1  4  7 10  3  6  9 12 11  8 17 14 13 16 19 22 15 18
   7  4  1  2  5 12  8  6  3 10 13 14 17  8 11 18 15 22 19 16
  12  5  2  1  4  7 14 13 10  3  6  8 22 15 18 11  8 17 24 23
  14  7  4  1  2  5 12 15 22  8  6  3 10 13 20 23 24 17  8 11
  15 12  5  2  1  4  7 14 23 20 13 10  3  6  8 22 25 28 31 18
(Column 3) = (3,4,2,1,1,2,4,5,7,12,23,...) in which the numbers 1,2,4 occur more than once.
		

Crossrefs

Cf. A007062, A309977.

Programs

Mathematica

a = Range[x = 40000]; rows = Table[a = Flatten[Map[Reverse, Partition[a, n]]], {n,
   NestWhile[# + 1 &, 1, (x = # Floor[x/#]) > 0 &] - 1}];
Flatten[Table[{Length[Select[SortBy[Tally[Map[#[[col]] &, rows]], #[[2]] &], #[[2]] > 1 &]]}, {col, 100}]]  (* Peter J. C. Moses, May 01 2023 *)