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

Author

Marco Ripà, Aug 10 2015

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A005115, A002110, A204189.

Programs

Magma

[11410337850553+(n-1)*4609098694200: n in [1..20]];

Mathematica

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

PARI

Vec(-x*(10949427981133*x-11410337850553) / (x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Sage

[11410337850553+(n-1)*4609098694200 for n in (1..20)]

Formula

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

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