A354485 Triangle read by rows: row n gives the arithmetic progression of exactly n primes with minimal final term, cf. A354376.

2, 2, 3, 3, 5, 7, 7, 19, 31, 43, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 7, 157, 307, 457, 607, 757, 907, 881, 1091, 1301, 1511, 1721, 1931, 2141, 2351, 3499, 3709, 3919, 4129, 4339, 4549, 4759, 4969, 5179, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089

Offset: 1

Author

Bernard Schott, May 29 2022

Keywords

• nonn
• tabl

Comments

For the corresponding values of the first term, the last term and the common difference of these arithmetic progressions, see respectively A354377, A354376 and A354484.

Without "exactly", we get A133277.

The primes in these arithmetic progressions need not be consecutive. (The smallest prime at the start of a run of exactly n consecutive primes in arithmetic progressions is A006560(n).)

Examples

			Triangle begins:
    2;
    2,    3;
    3,    5,    7;
    7,   19,   31,   43;
    5,   11,   17,   23,   29;
    7,   37,   67,   97,  127,  157;
    7,  157,  307,  457,  607,  757,  907;
  881, 1091, 1301, 1511, 1721, 1931, 2141, 2351;
  ...
		

References

• Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section A5, Arithmetic progressions of primes, pp. 25-28.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..231 (using A354376 and A354377)

Crossrefs

Cf. A006560, A133277, A354376, A354377, A354484.

Formula

T(n, 1) = A354377.

T(n, n) = A354376.