A023357 Primes that remain prime through 5 iterations of the function f(x) = 10x + 9.

13, 293, 6089, 12823, 37967, 40949, 121687, 192037, 243487, 379679, 409499, 471841, 1006193, 1217131, 1397311, 1438793, 1503613, 1541063, 1754591, 2058629, 2088421, 2346791, 2360357, 2428243, 2458609, 2621527, 2646167, 2721053, 3223247, 3280003

Offset

1,1

Comments

p, 10*p + 9, 100*p + 99, 1000*p + 999, 10000*p + 9999 and 100000*p + 99999 are prime for each term p. - Vincenzo Librandi, Aug 05 2010

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Formula

a(n) == 13 (mod 14). - John Cerkan, Aug 26 2016

Example

13 * 10 + 9 = 139, which is prime.
139 * 10 + 9 = 1399, which is also prime.
1399 * 10 + 9 = 13999, which is also prime.
13999 * 10 + 9 = 139999, which is also prime.
139999 * 10 + 9 = 1399999, which is also prime.
1399999 * 10 + 9 = 13999999 = 13 * 503 * 2141. This is the sixth iteration, but only five iterations are needed for 13 to be in the sequence.
17 * 10 + 9 = 179, which is prime.
179 * 10 + 9 = 1799 = 7 * 257. As this falls short of the five iterations needed, 17 is not in the sequence.

Mathematica

Select[Prime@ Range[10^6], Times @@ Boole@ PrimeQ@ NestList[10 # + 9 &, #, 5] > 0 &] (* Michael De Vlieger, Aug 26 2016 *)
(* The following program uses the AllTrue function from Mathematica version 10 *) Select[Prime[Range[250000]], AllTrue[Rest[NestList[10# + 9 &, #, 5]], PrimeQ]&] (* Harvey P. Dale, Jul 31 2018 *)

Prog

(Magma) [n: n in [1..19000000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999) and IsPrime(10000*n+9999) and IsPrime(100000*n+99999)] // Vincenzo Librandi, Aug 05 2010
(PARI) is(n)=isprime(n) && isprime(10*n+9) && isprime(100*n+99) && isprime(1000*n+999) && isprime(10000*n+9999) && isprime(100000*n+99999) \\ Charles R Greathouse IV, Jul 28 2016

Crossrefs

Sequence in context: A228753 A249864 A246462 * A165218 A317632 A076130

Adjacent sequences: A023354 A023355 A023356 * A023358 A023359 A023360

Keyword

nonn

Author

David W. Wilson

Status

approved