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

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

Offset: 1

Author

Marco Ripà, Aug 10 2015

Keywords

• nonn
• easy

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.

Examples

			a(24) = 515486946529943 + 23*30526020494970 = 1217585417914253 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

[515486946529943+(n-1)*30526020494970: n in [1..20]];

Mathematica

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

PARI

Vec(-x*(484960926034973*x-515486946529943)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Sage

[515486946529943+(n-1)*30526020494970 for n in (1..20)] #

Formula

a(n) = 515486946529943 + (n-1)*136831*A002110(9).

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