A118469 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 ).

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

Offset: 1

Author

Roger L. Bagula, May 04 2006

Keywords

• nonn
• tabl

Comments

An improved triangular Goldbach sequence in which the gap sum is taken from a start at n.

Examples

			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
		

Crossrefs

Main diagonal: A078444, 2nd diagonal: A073273.

Columns 1-8: A000012, A006254, A098090, A089253, A097069, A097338, A097480, A098605.

Programs

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