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A324799
Symmetric square array read by antidiagonals: T(n,k) = p(n)*p(k)-p(n*k), where p(i) = prime(i), for n>=1, k>=1.
2
2, 3, 3, 5, 2, 5, 7, 2, 2, 7, 11, 2, 2, 2, 11, 13, 4, -2, -2, 4, 13, 17, 2, 8, -4, 8, 2, 17, 19, 8, 4, 6, 6, 4, 8, 19, 23, 4, 12, 2, 24, 2, 12, 4, 23, 29, 8, 6, 12, 30, 30, 12, 6, 8, 29, 31, 16, 12, 2, 38, 18, 38, 2, 12, 16, 31, 37, 14, 32, 10, 36, 40, 40, 36, 10, 32, 14, 37, 41, 22, 18, 30, 56, 24, 62, 24, 56, 30, 18, 22, 41
OFFSET
1,1
COMMENTS
Mitrinovic et al. appear to assert that T(n,k) > 0 for all n,k, but presumably they should have said T(n,k) > 0 for all n+k >= 8.
REFERENCES
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.18, p. 247.
LINKS
H. Ishikawa, Über die Verteilung der Primzahlen, Sci. Rep. Tokyo Univ. Lit. Sci. Sect. A, 2 (1934), 27-40.
EXAMPLE
The first few antidiagonals are:
2,
3, 3,
5, 2, 5,
7, 2, 2, 7,
11, 2, 2, 2, 11,
13, 4, -2, -2, 4, 13,
17, 2, 8, -4, 8, 2, 17,
19, 8, 4, 6, 6, 4, 8, 19,
23, 4, 12, 2, 24, 2, 12, 4, 23,
29, 8, 6, 12, 30, 30, 12, 6, 8, 29,
31, 16, 12, 2, 38, 18, 38, 2, 12, 16, 31,
...
CROSSREFS
Main diagonal of the square array is A123914.
Sequence in context: A049272 A181483 A205130 * A069461 A329071 A232932
KEYWORD
sign,tabl,look
AUTHOR
N. J. A. Sloane, Sep 11 2019
STATUS
approved