A261151 a(n) = 11410337850553 + (n-1)*4609098694200.

11410337850553, 11871247719973, 12332157589393, 12793067458813, 13253977328233, 13714887197653, 14175797067073, 14636706936493, 15097616805913, 15558526675333, 16019436544753, 16480346414173, 16941256283593, 17402166153013, 17863076022433, 18323985891853

Offset

1,1

Comments

The terms n = 1..22 are prime. This is the longest known sequence of 22 primes in arithmetic progression with minimal end known as of August 10, 2015.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Jens Kruse Andersen, All known AP24 to AP26.

Wikipedia, Largest known primes in AP.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 11410337850553 + (n-1)*475180*A002110(8).

G.f.: -x*(10949427981133*x-11410337850553) / (x-1)^2. - Colin Barker, Aug 25 2015

Example

a(22) = 11410337850553 + 21*4609098694200 = 108201410428753 is prime.

Mathematica

Table[11410337850553 + (n - 1) 4609098694200, {n, 1, 20}]

Prog

(Sage) [11410337850553+(n-1)*4609098694200 for n in (1..20)]
(Magma) [11410337850553+(n-1)*4609098694200: n in [1..20]];
(PARI) Vec(-x*(10949427981133*x-11410337850553) / (x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Crossrefs

Cf. A005115, A002110, A204189.

Sequence in context: A257141 A250492 A095429 * A103575 A172551 A172615

Adjacent sequences: A261148 A261149 A261150 * A261152 A261153 A261154

Keyword

nonn,easy

Author

Marco Ripà, Aug 10 2015

Status

approved