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

1,2

Links

Table of n, a(n) for n=1..67.

Example

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.

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 *)

Crossrefs

Cf. A007062, A309977.

Sequence in context: A331857 A073138 A342179 * A367964 A214965 A350786

Adjacent sequences: A362810 A362811 A362812 * A362814 A362815 A362816

Keyword

nonn

Author

Clark Kimberling, May 04 2023

Status

approved