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A118469
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Triangle read by rows: a(n,m) = If(n = 1, then 1, else Prime(n) - 1 + Sum_{k=n..m} (Prime(k + 1) - Prime(k))/2.
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0
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1, 1, 3, 1, 4, 5, 1, 6, 7, 8, 1, 7, 8, 9, 11, 1, 9, 10, 11, 13, 14, 1, 10, 11, 12, 14, 15, 17, 1, 12, 13, 14, 16, 17, 19, 20, 1, 15, 16, 17, 19, 20, 22, 23, 25, 1, 16, 17, 18, 20, 21, 23, 24, 26, 29, 1, 19, 20, 21, 23, 24, 26, 27, 29, 32, 33, 1, 21, 22, 23, 25, 26, 28, 29, 31, 34, 35
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| An improved triangular Goldbach sequence in which the gap sum is taken from a start at n.
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EXAMPLE
| 1
1, 3
1, 4, 5
1, 6, 7, 8
1, 7, 8, 9, 11
1, 9, 10, 11, 13, 14
1, 10, 11, 12, 14, 15, 17
1, 12, 13, 14, 16, 17, 19, 20
1, 15, 16, 17, 19, 20, 22, 23, 25
1, 16, 17, 18, 20, 21, 23, 24, 26, 29
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MATHEMATICA
| t[n_, m_] := If[n == 1, 1, Prime[n] + Sum[(Prime[k + 1] - Prime[k])/2, {k, n, m}] - 1]; Table[ t[n, m], {m, 11}, {n, m}] // Flatten
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CROSSREFS
| Main diagonal: A078444, 2nd diagonal: A073273.
Columns 1-8: A000012, A006254, A098090, A089253, A097069, A097338, A097480, A098605.
Sequence in context: A016473 A029637 A097207 * A198553 A069203 A046070
Adjacent sequences: A118466 A118467 A118468 * A118470 A118471 A118472
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), May 04 2006
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