A261140 a(n) = 3486107472997423 + (n-1)*371891575525470.

3486107472997423, 3857999048522893, 4229890624048363, 4601782199573833, 4973673775099303, 5345565350624773, 5717456926150243, 6089348501675713, 6461240077201183, 6833131652726653, 7205023228252123, 7576914803777593, 7948806379303063, 8320697954828533

Offset: 1

Author

Marco Ripà, Aug 10 2015

Keywords

• nonn
• easy

Comments

The terms n = 1..26 are prime. This is the longest sequence of primes in arithmetic progression with smallest end, a(26)=12783396861134173, known as of August 10, 2015.

Examples

			a(26) = 3486107472997423 + 25*371891575525470 = 12783396861134173 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. A002110, A033188, A033290, A204189, A260751, A327760, A363980, A374949.

Programs

Magma

[3486107472997423+(n-1)*371891575525470: n in [1..20]];

Mathematica

Table[3486107472997423 + (n - 1) 371891575525470, {n, 1, 20}]
LinearRecurrence[{2,-1},{3486107472997423,3857999048522893},20] (* Harvey P. Dale, May 14 2022 *)

PARI

Vec(-x*(3114215897471953*x-3486107472997423)/(x-1)^2 + O(x^40)) \\ Colin Barker, Aug 25 2015

Formula

a(n) = 3486107472997423 + (n-1)*1666981*A002110(9).

G.f.: -x*(3114215897471953*x-3486107472997423) / (x-1)^2. - Colin Barker, Aug 25 2015