OFFSET
1,2
COMMENTS
Is this a permutation of the positive integers?
Conjectures from N. J. A. Sloane, Apr 22 2005: (Start)
"Call a number "postponed" if it cannot be placed right away, that is, if it is relatively prime to the numbers in the previous row. Then I conjecture that:
"(1) a number n >= 4 is postponed iff n is prime,
"(2) every number appears,
"(3) the primes appear in order,
"(4) 2p (p prime) will appear in one row and p will appear in the next row,
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11628 (rows 1 <= n <= 150).
EXAMPLE
Triangle begins:
1;
2, 3;
4, 6, 8;
9, 10, 12, 14;
5, 7, 15, 16, 18;
20, 21, 22, 24, 25, 26;
11, 13, 27, 28, 30, 32, 33;
...
7 is in the 5th row because it does not occur earlier and 14 is in the 4th row.
MATHEMATICA
f[w_List] := Block[{k = 4, m = {}}, Do[While[Nand[FreeQ[Join[w, m], k], AnyTrue[Last@ w, GCD[k, #] > 1 &]], k++]; AppendTo[m, k], {i, Length@ w + 1}]; m]; Nest[Append[#, f@ #] &, Table[n + k - 1, {n, 2}, {k, n}], 10] // Flatten (* Michael De Vlieger, Sep 25 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Leroy Quet, Jan 25 2005
EXTENSIONS
More terms from Joshua Zucker, May 20 2006
STATUS
approved