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 A212210 Triangle read by rows: T(n,k) = pi(n) + pi(k) - pi(n+k), n >= 1, 1 <= k <= n, where pi() = A000720(). 9
 -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, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A000720, A212211, A212212, A212213, A060208, A047885, A047886. Left diagonal is -A010051. Sequence in context: A291954 A339885 A106799 * A127499 A198068 A121361 Adjacent sequences:  A212207 A212208 A212209 * A212211 A212212 A212213 KEYWORD sign,tabl,nice AUTHOR N. J. A. Sloane, May 04 2012 STATUS approved

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)