A261150 a(n) = 403185216600637 + (n-1)*2124513401010.

403185216600637, 405309730001647, 407434243402657, 409558756803667, 411683270204677, 413807783605687, 415932297006697, 418056810407707, 420181323808717, 422305837209727, 424430350610737, 426554864011747, 428679377412757, 430803890813767, 432928404214777

Offset: 1

Author

Marco Ripà, Aug 10 2015

Keywords

• nonn
• easy

Comments

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.

Examples

			a(23) = 403185216600637 + 22*2124513401010 = 449924511422857 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

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

Mathematica

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

PARI

Vec(-x*(401060703199627*x-403185216600637)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Sage

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

Formula

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

G.f.: -x*(401060703199627*x-403185216600637) / (x-1)^2. - Colin Barker, Aug 25 2015