|
|
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 ).
|
|
0
|
|
|
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;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
An improved triangular Goldbach sequence in which the gap sum is taken from a start at n.
|
|
LINKS
|
|
|
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
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|