A317164 a(n) = 55837783597462913 + (n-1)*13858932213216090.

55837783597462913, 69696715810679003, 83555648023895093, 97414580237111183, 111273512450327273, 125132444663543363, 138991376876759453, 152850309089975543, 166709241303191633, 180568173516407723, 194427105729623813, 208286037942839903, 222144970156055993

Offset: 1

Author

Marco Ripà, Jul 23 2018

Keywords

• nonn
• easy

Comments

The terms for n = 1..26 are prime. As of Jul 23 2018, this is one of the longest known sequences of primes in arithmetic progression.

Examples

			a(26) = 55837783597462913 + 25*62121807*223092870 = 402311088927865163 is prime.
		

Links

• Jens Kruse Andersen, All known AP24 to AP26.
• B. Green and T. Tao, The primes contain arbitrarily long arithmetic progressions, Annals of Math. 167 (2008), 481-547.
• PrimeGrid, AP26 Search.
• Eric Weisstein's World of Mathematics, Prime Arithmetic Progression.
• Wikipedia, Primes in arithmetic progression.

Crossrefs

Cf. A002110, A204189, A260751, A261140, A317163.

Programs

GAP

List([1..25],n->55837783597462913+(n-1)*13858932213216090); # Muniru A Asiru, Jul 24 2018

Maple

seq(55837783597462913+(n-1)*13858932213216090,n=1..15); # Muniru A Asiru, Jul 24 2018

Mathematica

Table[55837783597462913 + (n - 1) 13858932213216090, {n, 1, 25}]

Formula

a(n) = 455837783597462913 + a(n-1)*62121807*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.