A226835 Triangle whose n-th row has the smallest n 3-almost primes in an arithmetic progression.

8, 8, 12, 12, 20, 28, 20, 44, 68, 92, 20, 44, 68, 92, 116, 402, 410, 418, 426, 434, 442, 266, 370, 474, 578, 682, 786, 890, 266, 370, 474, 578, 682, 786, 890, 994, 1270, 1414, 1558, 1702, 1846, 1990, 2134, 2278, 2422, 1394, 1586, 1778, 1970, 2162, 2354, 2546, 2738, 2930, 3122

Offset: 1

Author

T. D. Noe and Jonathan Vos Post, Jun 30 2013

Keywords

• nonn
• tabl

Comments

Note that this triangle (at least for all n <= 29) is twice A226833, which is the similar triangle of semiprimes.

Examples

			Triangle:
8,
8,    12,
12,   20,   28,
20,   44,   68,   92,
20,   44,   68,   92,   116,
402,  410,  418,  426,  434,  442,
266,  370,  474,  578,  682,  786,  890,
266,  370,  474,  578,  682,  786,  890,  994,
1270, 1414, 1558, 1702, 1846, 1990, 2134, 2278, 2422,
1394, 1586, 1778, 1970, 2162, 2354, 2546, 2738, 2930, 3122
		

Crossrefs

Cf. A226833 (similar triangle of semiprimes).

Programs

Mathematica

TriPrimeQ[n_Integer] := If[Abs[n] < 2, False, (3 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; p3 = Select[Range[4000], TriPrimeQ]; nn = Length[p3]; t = {}; n = 0; last = 1; While[n++; found = False; last = n; While[k = last - 1; p3Short = Take[p3, last]; While[d = p3[[last]] - p3[[k]]; nums = Table[p3[[last]] - i*d, {i, 0, n - 1}]; int = Intersection[nums, p3Short]; nums[[-1]] > 0 && Length[int] < n, k--]; nums[[-1]] <= 0 && last < nn, last++]; If[last < nn, AppendTo[t, Reverse[nums]]]; last < nn]; t