OFFSET
1,15
COMMENTS
It is conjectured that pi(x)+pi(y) >= pi(x+y) for 1 < y <= x.
A006093 gives row numbers of rows containing at least one negative term. [Reinhard Zumkeller, May 05 2012]
REFERENCES
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.5, p. 235.
LINKS
Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened
P. Erdos and J. L. Selfridge, Complete prime subsets of consecutive integers. Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971), pp. 1--14. Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971. MR0337828 (49 #2597).
EXAMPLE
Triangle begins:
-1
-1 0
0 0 1
-1 0 0 0
0 0 1 1 2
-1 0 1 1 1 1
0 1 2 1 2 1 2
0 1 1 1 1 1 2 2
0 0 1 0 1 1 2 1 1
-1 0 0 0 1 1 1 1 0 0
...
MATHEMATICA
t[n_, k_] := PrimePi[n] + PrimePi[k] - PrimePi[n + k]; Table[t[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 17 2012 *)
PROG
(Haskell)
import Data.List (inits, tails)
a212210 n k = a212210_tabl !! (n-1) !! (k-1)
a212210_row n = a212210_tabl !! (n-1)
a212210_tabl = f $ tail $ zip (inits pis) (tails pis) where
f ((xs, ys) : zss) = (zipWith (-) (map (+ last xs) (xs)) ys) : f zss
pis = a000720_list
-- Reinhard Zumkeller, May 04 2012
CROSSREFS
KEYWORD
AUTHOR
N. J. A. Sloane, May 04 2012
STATUS
approved