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A317259 a(n) = 136926916457315893 + (n - 1)*9843204333812850.

%I A317259 #13 Feb 16 2025 08:33:56
%S A317259 136926916457315893,146770120791128743,156613325124941593,
%T A317259 166456529458754443,176299733792567293,186142938126380143,
%U A317259 195986142460192993,205829346794005843,215672551127818693,225515755461631543,235358959795444393,245202164129257243,255045368463070093
%N A317259 a(n) = 136926916457315893 + (n - 1)*9843204333812850.
%C A317259 The terms for n = 1..26 are prime. As of Jul 25 2018, this is one of the longest known sequences of primes in arithmetic progression.
%C A317259 a(27) = 392850229136449993 = 41 * 179 * 53529122378587.
%C A317259 To date, an arithmetic sequence of 27 primes has not been found yet.
%H A317259 Jens Kruse Andersen, <a href="http://primerecords.dk/aprecords.htm#ap24">All known AP24 to AP26</a>.
%H A317259 B. Green and T. Tao, <a href="http://arxiv.org/abs/math.NT/0404188">The primes contain arbitrarily long arithmetic progressions</a>, Annals of Math. 167 (2008), 481-547.
%H A317259 PrimeGrid, <a href="http://www.primegrid.com/download/AP26.pdf">AP26 Search</a>.
%H A317259 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeArithmeticProgression.html">Prime Arithmetic Progression</a>.
%H A317259 Wikipedia, <a href="http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%e A317259 a(26) = 136926916457315893 + 25*44121555*223092870 = 383007024802637143 is prime.
%p A317259 seq(136926916457315893+(n-1)*9843204333812850,n=1..25);
%t A317259 Table[136926916457315893 + (n - 1) 9843204333812850, {n, 1, 25}]
%o A317259 (GAP) List([1..25], n->136926916457315893+(n-1)*9843204333812850);
%Y A317259 Cf. A002120, A204189, A260751, A261140, A317163, A317164.
%K A317259 nonn,easy
%O A317259 1,1
%A A317259 _Marco Ripà_, Jul 25 2018
%E A317259 a(7) corrected by _Georg Fischer_, Mar 13 2020