cp's OEIS Frontend

A226833 Triangle whose n-th row has the smallest n semiprimes in an arithmetic progression.

%I A226833 #19 Jul 29 2019 11:50:49
%S A226833 4,4,6,6,10,14,10,22,34,46,10,22,34,46,58,201,205,209,213,217,221,133,
%T A226833 185,237,289,341,393,445,133,185,237,289,341,393,445,497,635,707,779,
%U A226833 851,923,995,1067,1139,1211,697,793,889,985,1081,1177,1273,1369,1465,1561
%N A226833 Triangle whose n-th row has the smallest n semiprimes in an arithmetic progression.
%C A226833 The largest term of each row is as small as possible. Although Nowicki reports on the 28th row of this triangle, those terms are too large. Sequence A096003 reports the largest terms.
%H A226833 T. D. Noe, <a href="/A226833/b226833.txt">Rows n = 1..32 of triangle, flattened</a>
%H A226833 Andrzej Nowicki, <a href="http://arxiv.org/abs/1306.6424">Second numbers in arithmetic progressions</a>, arxiv 1306.6424
%e A226833 Triangle:
%e A226833 4,
%e A226833 4,   6,
%e A226833 6,   10,  14,
%e A226833 10,  22,  34,  46,
%e A226833 10,  22,  34,  46,  58,
%e A226833 201, 205, 209, 213, 217,  221,
%e A226833 133, 185, 237, 289, 341,  393,  445,
%e A226833 133, 185, 237, 289, 341,  393,  445,  497,
%e A226833 635, 707, 779, 851, 923,  995,  1067, 1139, 1211,
%e A226833 697, 793, 889, 985, 1081, 1177, 1273, 1369, 1465, 1561
%t A226833 SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; p2 = Select[Range[2000], SemiPrimeQ]; nn = Length[p2]; t = {}; n = 0; last = 1; While[n++; found = False; last = n; While[k = last - 1; While[d = p2[[last]] - p2[[k]]; nums = Table[p2[[last]] - i*d, {i, 0, n - 1}]; int = Intersection[nums, Take[p2, last]]; nums[[-1]] > 0 && Length[int] < n, k--]; nums[[-1]] <= 0 && last < nn, last++]; If[last < nn, AppendTo[t, Reverse[nums]]]; last < nn]; t
%Y A226833 Cf. A226834 (first term), A096003 (last term), A097824 (gaps).
%K A226833 nonn,tabl,look
%O A226833 1,1
%A A226833 _T. D. Noe_, Jun 28 2013