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

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

Offset

1,1

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.

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

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

Example

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

Mathematica

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

Prog

(Sage) [403185216600637+(n-1)*2124513401010 for n in (1..20)]
(Magma) [403185216600637+(n-1)*2124513401010: n in [1..20]];
(PARI) Vec(-x*(401060703199627*x-403185216600637)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Crossrefs

Cf. A005115, A002110, A204189.

Sequence in context: A198803 A317290 A128769 * A181392 A299799 A175531

Adjacent sequences: A261147 A261148 A261149 * A261151 A261152 A261153

Keyword

nonn,easy

Author

Marco Ripà, Aug 10 2015

Status

approved