cp's OEIS Frontend

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

%I A354377 #16 May 27 2022 08:12:59
%S A354377 2,2,3,7,5,7,7,881,3499,199,75307,110437,4943,31385539,115453391,
%T A354377 53297929,3430751869,4808316343,8297644387,214861583621,5749146449311
%N A354377 Initial terms associated with the arithmetic progressions of primes of A354376.
%C A354377 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 A354377 The adverb "exactly" requires both i-d and i+n*d to be nonprime (see A113827).
%C A354377 For the corresponding values of the last term, see A354376.
%C A354377 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 A354377 a(n) != A113827(n) for n = 4, 8, 9, 11. - _Michael S. Branicky_, May 26 2022
%D A354377 R. K. Guy, Unsolved Problems in Number Theory, A5, Arithmetic progressions of primes.
%e A354377 The first few corresponding arithmetic progressions are:
%e A354377 n = 1 (2);
%e A354377 n = 2 (2, 3);
%e A354377 n = 3 (3, 5, 7);
%e A354377 n = 4 (7, 19, 31, 43);
%e A354377 n = 5 (5, 11, 17, 23, 29);
%e A354377 n = 6 (7, 37, 67, 97, 127, 157);
%e A354377 n = 7 (7, 157, 307, 457, 607, 757, 907)...
%Y A354377 Cf. A006560, A113827, A354376.
%K A354377 nonn,more
%O A354377 1,1
%A A354377 _Bernard Schott_, May 26 2022
%E A354377 a(8)-a(21) from _Michael S. Branicky_, May 26 2022