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A226833 Triangle whose n-th row has the smallest n semiprimes in an arithmetic progression. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl,look
AUTHOR
T. D. Noe, Jun 28 2013
STATUS
approved

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Last modified March 29 03:39 EDT 2024. Contains 371264 sequences. (Running on oeis4.)