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A317164
a(n) = 55837783597462913 + (n-1)*13858932213216090.
3
55837783597462913, 69696715810679003, 83555648023895093, 97414580237111183, 111273512450327273, 125132444663543363, 138991376876759453, 152850309089975543, 166709241303191633, 180568173516407723, 194427105729623813, 208286037942839903, 222144970156055993
OFFSET
1,1
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.
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.
FORMULA
a(n) = 455837783597462913 + a(n-1)*62121807*23#, where 23# := 2*3*5*7*11*13*17*19*23 = 223092870.
EXAMPLE
a(26) = 55837783597462913 + 25*62121807*223092870 = 402311088927865163 is prime.
MAPLE
seq(55837783597462913+(n-1)*13858932213216090, n=1..15); # Muniru A Asiru, Jul 24 2018
MATHEMATICA
Table[55837783597462913 + (n - 1) 13858932213216090, {n, 1, 25}]
PROG
(GAP) List([1..25], n->55837783597462913+(n-1)*13858932213216090); # Muniru A Asiru, Jul 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Marco Ripà, Jul 23 2018
STATUS
approved