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

Author

Bernard Schott, May 26 2022

Keywords

• nonn
• more

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

Examples

			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)...
		

References

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

Crossrefs

Cf. A006560, A113827, A354376.

Extensions

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