A354377 - OEIS

%I #16 May 27 2022 08:12:59

%S 2,2,3,7,5,7,7,881,3499,199,75307,110437,4943,31385539,115453391,

%T 53297929,3430751869,4808316343,8297644387,214861583621,5749146449311

%N Initial terms associated with the arithmetic progressions of primes of A354376.

%C 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.

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

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

%C 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).)

%C a(n) != A113827(n) for n = 4, 8, 9, 11. - _Michael S. Branicky_, May 26 2022

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

%e The first few corresponding arithmetic progressions are:

%e n = 1 (2);

%e n = 2 (2, 3);

%e n = 3 (3, 5, 7);

%e n = 4 (7, 19, 31, 43);

%e n = 5 (5, 11, 17, 23, 29);

%e n = 6 (7, 37, 67, 97, 127, 157);

%e n = 7 (7, 157, 307, 457, 607, 757, 907)...

%Y Cf. A006560, A113827, A354376.

%K nonn,more

%O 1,1

%A _Bernard Schott_, May 26 2022

%E a(8)-a(21) from _Michael S. Branicky_, May 26 2022