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

1,1

Comments

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

Links

Table of n, a(n) for n=1..55.

Example

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

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

Crossrefs

Cf. A226833 (similar triangle of semiprimes).

Sequence in context: A219236 A259532 A329822 * A363326 A343526 A335896

Adjacent sequences: A226832 A226833 A226834 * A226836 A226837 A226838

Keyword

nonn,tabl

Author

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

Status

approved