A226835 - OEIS

%I #10 Jul 03 2013 20:21:34

%S 8,8,12,12,20,28,20,44,68,92,20,44,68,92,116,402,410,418,426,434,442,

%T 266,370,474,578,682,786,890,266,370,474,578,682,786,890,994,1270,

%U 1414,1558,1702,1846,1990,2134,2278,2422,1394,1586,1778,1970,2162,2354,2546,2738,2930,3122

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

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

%e Triangle:

%e 8,

%e 8,    12,

%e 12,   20,   28,

%e 20,   44,   68,   92,

%e 20,   44,   68,   92,   116,

%e 402,  410,  418,  426,  434,  442,

%e 266,  370,  474,  578,  682,  786,  890,

%e 266,  370,  474,  578,  682,  786,  890,  994,

%e 1270, 1414, 1558, 1702, 1846, 1990, 2134, 2278, 2422,

%e 1394, 1586, 1778, 1970, 2162, 2354, 2546, 2738, 2930, 3122

%t 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

%Y Cf. A226833 (similar triangle of semiprimes).

%K nonn,tabl

%O 1,1

%A _T. D. Noe_ and _Jonathan Vos Post_, Jun 30 2013