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 A212211 Triangle read by rows: T(n,k) = pi(n) + pi(k) - pi(n+k), n >= 2, 2 <= k <= n, where pi() = A000720(). 2
 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,10 COMMENTS It is conjectured that pi(x) + pi(y) >= pi(x+y) for 1 < y <= x. REFERENCES D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.5, p. 235. LINKS Reinhard Zumkeller, Rows n = 2..150 of triangle, flattened P. Erdős 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: 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... MATHEMATICA t[n_, k_] := PrimePi[n] + PrimePi[k] - PrimePi[n+k]; Flatten[ Table[t[n, k], {n, 2, 13}, {k, 2, n}]] (* Jean-François Alcover, May 21 2012 *) PROG (Haskell) a212211 n k = a212211_tabl !! (n-2) !! (k-2) a212211_tabl = map a212211_row [2..] a212211_row n = zipWith (-) (map (+ a000720 n) \$ take (n - 1) \$ tail a000720_list) (drop (n + 1) a000720_list) -- Reinhard Zumkeller, May 04 2012 CROSSREFS Cf. A000720, A212210, A212212, A212213, A060208, A047885, A047886. Sequence in context: A025914 A284977 A025916 * A321764 A333809 A306440 Adjacent sequences: A212208 A212209 A212210 * A212212 A212213 A212214 KEYWORD nonn,tabl,nice AUTHOR N. J. A. Sloane, May 04 2012 STATUS approved

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