A261149 a(n) = 515486946529943 + (n-1)*30526020494970.

515486946529943, 546012967024913, 576538987519883, 607065008014853, 637591028509823, 668117049004793, 698643069499763, 729169089994733, 759695110489703, 790221130984673, 820747151479643, 851273171974613, 881799192469583, 912325212964553, 942851233459523

Offset

1,1

Comments

The terms n = 1..24 are prime. This is the longest known sequence of 24 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) = 515486946529943 + (n-1)*136831*A002110(9).

G.f.: -x*(484960926034973*x-515486946529943) / (x-1)^2. - Colin Barker, Aug 25 2015

Example

a(24) = 515486946529943 + 23*30526020494970 = 1217585417914253 is prime.

Mathematica

Table[515486946529943 + (n - 1) 30526020494970, {n, 1, 20}]

Prog

(Sage) [515486946529943+(n-1)*30526020494970 for n in (1..20)] #
(Magma) [515486946529943+(n-1)*30526020494970: n in [1..20]];
(PARI) Vec(-x*(484960926034973*x-515486946529943)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Crossrefs

Cf. A005115, A002110, A204189.

Sequence in context: A172665 A172601 A086438 * A104873 A297450 A172585

Adjacent sequences: A261146 A261147 A261148 * A261150 A261151 A261152

Keyword

nonn,easy

Author

Marco Ripà, Aug 10 2015

Status

approved