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%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
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