A361748 Triangle T(n, k) of distinct positive integers, n > 0, k = 1..n, read by rows and filled in the greedy way such that T(n, k) is a multiple of T(n, 1).
1, 2, 4, 3, 6, 9, 5, 10, 15, 20, 7, 14, 21, 28, 35, 8, 16, 24, 32, 40, 48, 11, 22, 33, 44, 55, 66, 77, 12, 36, 60, 72, 84, 96, 108, 120, 13, 26, 39, 52, 65, 78, 91, 104, 117, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 18, 54, 90, 126, 144, 162, 180, 198, 216, 234, 252
Offset: 1
Examples
Triangle T(n, k) begins:
1;
2, 4;
3, 6, 9;
5, 10, 15, 20;
7, 14, 21, 28, 35;
8, 16, 24, 32, 40, 48;
11, 22, 33, 44, 55, 66, 77;
12, 36, 60, 72, 84, 96, 108, 120;
13, 26, 39, 52, 65, 78, 91, 104, 117;
17, 34, 51, 68, 85, 102, 119, 136, 153, 170;
...
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows n = 1..150)
- Rémy Sigrist, PARI program
- Index entries for sequences that are permutations of the natural numbers
Programs
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Mathematica
nn = 11; c[] = False; T[1, 1] = 1; c[1] = True; u = 2; Do[If[j == 1, k = u; m = 1, While[c[k m], m++]]; Set[{T[i, j], c[#]}, {#, True}] &[k m]; If[k == u, While[c[u], u++]], {i, 2, nn}, {j, i}]; Table[T[i, j], {i, nn}, {j, i}] // Flatten (* _Michael De Vlieger, Apr 01 2023 *)
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PARI
See Links section.
Formula
T(n, k) = k * T(n, 1) when T(n, 1) is a prime number.
Comments