A317259 a(n) = 136926916457315893 + (n - 1)*9843204333812850.

136926916457315893, 146770120791128743, 156613325124941593, 166456529458754443, 176299733792567293, 186142938126380143, 195986142460192993, 205829346794005843, 215672551127818693, 225515755461631543, 235358959795444393, 245202164129257243, 255045368463070093

Offset

1,1

Comments

The terms for n = 1..26 are prime. As of Jul 25 2018, this is one of the longest known sequences of primes in arithmetic progression.

a(27) = 392850229136449993 = 41 * 179 * 53529122378587.

To date, an arithmetic sequence of 27 primes has not been found yet.

Links

Table of n, a(n) for n=1..13.

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.

Example

a(26) = 136926916457315893 + 25*44121555*223092870 = 383007024802637143 is prime.

Maple

seq(136926916457315893+(n-1)*9843204333812850, n=1..25);

Mathematica

Table[136926916457315893 + (n - 1) 9843204333812850, {n, 1, 25}]

Prog

(GAP) List([1..25], n->136926916457315893+(n-1)*9843204333812850);

Crossrefs

Cf. A002120, A204189, A260751, A261140, A317163, A317164.

Sequence in context: A099727 A011530 A198801 * A317914 A317255 A261152

Adjacent sequences: A317256 A317257 A317258 * A317260 A317261 A317262

Keyword

nonn,easy

Author

Marco Ripà, Jul 25 2018

Extensions

a(7) corrected by Georg Fischer, Mar 13 2020

Status

approved