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

4, 4, 6, 6, 10, 14, 10, 22, 34, 46, 10, 22, 34, 46, 58, 201, 205, 209, 213, 217, 221, 133, 185, 237, 289, 341, 393, 445, 133, 185, 237, 289, 341, 393, 445, 497, 635, 707, 779, 851, 923, 995, 1067, 1139, 1211, 697, 793, 889, 985, 1081, 1177, 1273, 1369, 1465, 1561

Offset

1,1

Comments

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.

Links

T. D. Noe, Rows n = 1..32 of triangle, flattened

Andrzej Nowicki, Second numbers in arithmetic progressions, arxiv 1306.6424

Example

Triangle:
4,
4,   6,
6,   10,  14,
10,  22,  34,  46,
10,  22,  34,  46,  58,
201, 205, 209, 213, 217,  221,
133, 185, 237, 289, 341,  393,  445,
133, 185, 237, 289, 341,  393,  445,  497,
635, 707, 779, 851, 923,  995,  1067, 1139, 1211,
697, 793, 889, 985, 1081, 1177, 1273, 1369, 1465, 1561

Mathematica

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

Crossrefs

Cf. A226834 (first term), A096003 (last term), A097824 (gaps).

Sequence in context: A365216 A132882 A171384 * A262260 A203632 A278766

Adjacent sequences: A226830 A226831 A226832 * A226834 A226835 A226836

Keyword

nonn,tabl,look

Author

T. D. Noe, Jun 28 2013

Status

approved