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A317164 a(n) = 55837783597462913 + (n-1)*13858932213216090. 3

%I #13 Aug 06 2018 05:33:07

%S 55837783597462913,69696715810679003,83555648023895093,

%T 97414580237111183,111273512450327273,125132444663543363,

%U 138991376876759453,152850309089975543,166709241303191633,180568173516407723,194427105729623813,208286037942839903,222144970156055993

%N a(n) = 55837783597462913 + (n-1)*13858932213216090.

%C The terms for n = 1..26 are prime. As of Jul 23 2018, this is one of the longest known sequences of primes in arithmetic progression.

%H Jens Kruse Andersen, <a href="http://primerecords.dk/aprecords.htm#ap24">All known AP24 to AP26</a>.

%H 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 PrimeGrid, <a href="http://www.primegrid.com/download/AP26.pdf">AP26 Search</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeArithmeticProgression.html">Prime Arithmetic Progression</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.

%F a(n) = 455837783597462913 + a(n-1)*62121807*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.

%e a(26) = 55837783597462913 + 25*62121807*223092870 = 402311088927865163 is prime.

%p seq(55837783597462913+(n-1)*13858932213216090,n=1..15); # _Muniru A Asiru_, Jul 24 2018

%t Table[55837783597462913 + (n - 1) 13858932213216090, {n, 1, 25}]

%o (GAP) List([1..25],n->55837783597462913+(n-1)*13858932213216090); # _Muniru A Asiru_, Jul 24 2018

%Y Cf. A002110, A204189, A260751, A261140, A317163.

%K nonn,easy

%O 1,1

%A _Marco RipĂ _, Jul 23 2018

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)