A023355 Primes that remain prime through 5 iterations of function f(x) = 9x + 10.

103, 937, 4129, 17959, 21067, 38561, 113567, 125539, 179999, 215153, 225779, 293651, 310027, 324449, 341227, 384619, 454417, 458981, 491489, 505919, 521527, 526441, 535351, 612889, 640477, 672439, 766211, 791797, 837047, 849763, 873569

Offset

1,1

Comments

Primes p such that 9*p+10, 81*p+100, 729*p+910, 6561*p+8200 and 59049*p+73810 are also prime. - Vincenzo Librandi, Aug 05 2010

Links

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

Example

103 is in the sequence because it is prime, 9*103 + 10 = 937 is prime, 9*937 + 10 = 8443 is prime, 9*8443 + 10 = 75997 is prime, 9*75997 + 10 = 683983 is prime, and 9*683983 + 10 = 6155857 is prime. - Michael B. Porter, Aug 23 2016

Maple

A023355:=n->`if`(isprime(n) and isprime(9*n+10) and isprime(81*n+100) and isprime(729*n+910) and isprime(6561*n+8200) and isprime(59049*n+73810), n, NULL): seq(A023355(n), n=1..10^6); # Wesley Ivan Hurt, Aug 23 2016

Mathematica

Select[Prime[Range[70000]], AllTrue[Rest[NestList[9#+10&, #, 5]], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 24 2017 *)

Prog

(Magma) [n: n in [1..19000000] | IsPrime(n) and IsPrime(9*n+10) and IsPrime(81*n+100) and IsPrime(729*n+910) and IsPrime(6561*n+8200) and IsPrime(59049*n+73810)] // Vincenzo Librandi, Aug 05 2010

Crossrefs

Cf. A023299, A023327.

Sequence in context: A237611 A077405 A262758 * A113629 A034180 A076460

Adjacent sequences: A023352 A023353 A023354 * A023356 A023357 A023358

Keyword

nonn

Author

David W. Wilson

Status

approved