A212211 - OEIS

A212211

Triangle read by rows: T(n,k) = pi(n) + pi(k) - pi(n+k), n >= 2, 2 <= k <= n, where pi() = A000720().

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

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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, 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: A376631 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