A261150 - OEIS

%I #23 Sep 08 2022 08:46:13

%S 403185216600637,405309730001647,407434243402657,409558756803667,

%T 411683270204677,413807783605687,415932297006697,418056810407707,

%U 420181323808717,422305837209727,424430350610737,426554864011747,428679377412757,430803890813767,432928404214777

%N a(n) = 403185216600637 + (n-1)*2124513401010.

%C The terms n = 1..23 are prime. This is the longest known sequence of 23 primes in arithmetic progression with minimal end known as of August 10, 2015.

%H Colin Barker, <a href="/A261150/b261150.txt">Table of n, a(n) for n = 1..1000</a>

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression#Largest_known_primes_in_AP">Largest known primes in AP</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 403185216600637 + (n-1)*9523*A002110(9).

%F G.f.: -x*(401060703199627*x-403185216600637) / (x-1)^2. - _Colin Barker_, Aug 25 2015

%e a(23) = 403185216600637 + 22*2124513401010 = 449924511422857 is prime.

%t Table[403185216600637 + (n - 1) 2124513401010, {n, 1, 23}]

%o (Sage) [403185216600637+(n-1)*2124513401010 for n in (1..20)]

%o (Magma) [403185216600637+(n-1)*2124513401010: n in [1..20]];

%o (PARI) Vec(-x*(401060703199627*x-403185216600637)/(x-1)^2 + O(x^40)) \\ _Colin Barker_, Aug 25 2015

%Y Cf. A005115, A002110, A204189.

%K nonn,easy

%O 1,1

%A _Marco Ripà_, Aug 10 2015