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A212213
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Array read by antidiagonals: pi(n) + pi(k) - pi(n+k), where pi() = A000720.
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8
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0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0
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refs;
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internal format)
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OFFSET
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2,23
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COMMENTS
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It is conjectured that pi(x) + pi(y) >= pi(x+y) for 1 < y <= x.
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REFERENCES
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D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.5, p. 235.
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LINKS
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G. C. Greubel, Table of n, a(n) for the first 100 rows, 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.
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EXAMPLE
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Array begins:
0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, ...
0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, ...
0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, ...
0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, ...
1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, ...
...
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MATHEMATICA
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t[n_, k_] := PrimePi[n] + PrimePi[k] - PrimePi[n + k]; Table[t[n - k + 2, k], {n, 0, 15}, {k, 2, n}] // Flatten (* Jean-François Alcover, Dec 31 2012 *)
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CROSSREFS
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Cf. A000720, A047885, A047886, A060208, A212210-A212213.
Sequence in context: A072731 A221169 A212212 * A214339 A129174 A129175
Adjacent sequences: A212210 A212211 A212212 * A212214 A212215 A212216
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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N. J. A. Sloane, May 04 2012
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STATUS
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approved
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