A317914 a(n) = 142099325379199423 + (n-1)*3691994023167450.

142099325379199423, 145791319402366873, 149483313425534323, 153175307448701773, 156867301471869223, 160559295495036673, 164251289518204123, 167943283541371573, 171635277564539023, 175327271587706473, 179019265610873923

Offset: 1

Author

Marco Ripà, Aug 10 2018

Keywords

• easy
• nonn

Comments

The terms for n = 1..26 are prime. As of Aug 10 2018, this is one of the longest known sequences of primes in arithmetic progression.

Examples

			a(26) = 142099325379199423 + 25*16549135*223092870 = 234399175958385673 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, A317164.

Programs

GAP

List([1..26],n->142099325379199423+(n-1)*3691994023167450);

Maple

seq(142099325379199423+(n-1)*3691994023167450,n=1..26);

Mathematica

Table[142099325379199423 + (n - 1) 3691994023167450, {n, 1, 26}]

Formula

a(n) = 142099325379199423 + a(n-1)*16549135*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.