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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
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
Sequence in context: A025914 A284977 A025916 * A321764 A333809 A306440
KEYWORD
nonn,tabl,nice
AUTHOR
N. J. A. Sloane, May 04 2012
STATUS
approved

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Last modified May 24 15:32 EDT 2024. Contains 372778 sequences. (Running on oeis4.)