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

1,1

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).)

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)

Formula

T(n, 1) = A354377.

T(n, n) = A354376.

Example

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;
  ...

Crossrefs

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

Sequence in context: A130791 A133277 A133276 * A055501 A096010 A241507

Adjacent sequences: A354482 A354483 A354484 * A354486 A354487 A354488

Keyword

nonn,tabl

Author

Bernard Schott, May 29 2022

Status

approved