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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

Erdos, P.; Selfridge, J. L. 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)

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

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-Fran├žois 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, A212210-A212213, A060208, A047885, A047886. Left diagonal is -A010051.

Sequence in context: A255237 A291954 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 August 15 09:12 EDT 2018. Contains 313756 sequences. (Running on oeis4.)