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, 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

Seiichi Manyama, Antidiagonals n = 1..140, flattened

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

Adjacent sequences: A324796 A324797 A324798 * A324800 A324801 A324802

Keyword

sign,tabl,look

Author

N. J. A. Sloane, Sep 11 2019

Status

approved