A357431 Triangle read by rows where each term in row n is the next greater multiple of n..1.

1, 2, 3, 3, 4, 5, 4, 6, 8, 9, 5, 8, 9, 10, 11, 6, 10, 12, 15, 16, 17, 7, 12, 15, 16, 18, 20, 21, 8, 14, 18, 20, 24, 27, 28, 29, 9, 16, 21, 24, 25, 28, 30, 32, 33, 10, 18, 24, 28, 30, 35, 36, 39, 40, 41, 11, 20, 27, 32, 35, 36, 40, 44, 45, 46, 47

Offset

1,2

Comments

Row n has length n and columns are numbered k = 1..n.

Row n begins with n which is trivially divisible by n. This is followed by the least number greater than n that is divisible by n-1. Next comes the least number that is greater than this preceding one and is divisible by n-2. Then it continues the same way until the last one is reached, which is trivially divisible by 1.

The end-most terms of the rows are A007952.

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..9870 (first 140 rows flattened)

Formula

T(n,1) = n.

T(n,k) = T(n,k-1) + (n-k+1) - (T(n,k-1) mod (n-k+1)), for k >= 2.

T(n,n) = A007952(n).

Example

Triangle begins:
  n/k|  1   2   3   4   5   6   7
  --------------------------------
  1  |  1;
  2  |  2,  3;
  3  |  3,  4,  5;
  4  |  4,  6,  8,  9;
  5  |  5,  8,  9, 10, 11;
  6  |  6, 10, 12, 15, 16, 17;
  7  |  7, 12, 15, 16, 18, 20, 21;
  ...
For row n=6, the numbers of the chain, and below them their divisors are:
  6 10 12 15 16 17
  6  5  4  3  2  1

Mathematica

row[n_] := Module[{k = n, s = Table[0, n], r}, s[[1]] = n; Do[k++; k += If[(r = Mod[k, i]) == 0, 0, i - Mod[k, i]]; s[[n+1-i]] = k, {i, n - 1, 1, -1}]; s]; Array[row, 11] // Flatten (* Amiram Eldar, Sep 28 2022 *)

Prog

(PARI) row(n) = my(v=vector(n)); v[1] = n; for (k=2, n, v[k] = v[k-1] + (n-k+1) - (v[k-1] % (n-k+1)); ); v; \\ Michel Marcus, Nov 16 2022

Crossrefs

Cf. A357417 (row sums), A357498, A007952 (right diagonal).

Sequence in context: A335680 A026354 A179840 * A361383 A240153 A241435

Adjacent sequences: A357428 A357429 A357430 * A357432 A357433 A357434

Keyword

nonn,tabl

Author

Tamas Sandor Nagy, Sep 28 2022

Status

approved