A354377 Initial terms associated with the arithmetic progressions of primes of A354376.

2, 2, 3, 7, 5, 7, 7, 881, 3499, 199, 75307, 110437, 4943, 31385539, 115453391, 53297929, 3430751869, 4808316343, 8297644387, 214861583621, 5749146449311

Offset

1,1

Comments

Equivalently: Let i, i+d, i+2d, ..., i+(n-1)d be an arithmetic progression of exactly n primes; choose the one which minimizes the last term; then a(n) = first term i.

The adverb "exactly" requires both i-d and i+n*d to be nonprime (see A113827).

For the corresponding values of the last term, see A354376.

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 progression is A006560(n).)

a(n) != A113827(n) for n = 4, 8, 9, 11. - Michael S. Branicky, May 26 2022

References

R. K. Guy, Unsolved Problems in Number Theory, A5, Arithmetic progressions of primes.

Links

Table of n, a(n) for n=1..21.

Example

The first few corresponding arithmetic progressions are:
n = 1 (2);
n = 2 (2, 3);
n = 3 (3, 5, 7);
n = 4 (7, 19, 31, 43);
n = 5 (5, 11, 17, 23, 29);
n = 6 (7, 37, 67, 97, 127, 157);
n = 7 (7, 157, 307, 457, 607, 757, 907)...

Crossrefs

Cf. A006560, A113827, A354376.

Sequence in context: A267822 A210598 A330728 * A051301 A002583 A068519

Adjacent sequences: A354374 A354375 A354376 * A354378 A354379 A354380

Keyword

nonn,more

Author

Bernard Schott, May 26 2022

Extensions

a(8)-a(21) from Michael S. Branicky, May 26 2022

Status

approved