A023270 -id:A023270 - cp's OEIS frontend

A023301 Primes that remain prime through 3 iterations of function f(x) = 10x + 9.

13, 139, 293, 331, 547, 967, 1049, 1399, 1567, 1889, 1997, 2087, 2137, 2309, 2423, 2437, 2753, 2939, 3719, 3761, 3919, 4451, 4517, 4621, 6089, 7001, 7741, 8423, 8849, 9437, 10487, 11657, 12007, 12347, 12823, 13469, 15289, 15373, 15661, 17737, 17989

Offset: 1

David W. Wilson

nonn

Primes p such that 10*p+9, 100*p+99 and 1000*p+999 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023240, A023270, and A102700.

[n: n in [1..450000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999)] // Vincenzo Librandi, Aug 04 2010

nrp3Q[n_]:=AllTrue[Rest[NestList[10#+9&,n,3]],PrimeQ]; Select[Prime[ Range[ 2100]],nrp3Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2019 *)

A023329 Primes that remain prime through 4 iterations of function f(x) = 10x + 9.

Original entry on oeis.org

13, 139, 293, 1889, 2939, 3719, 6089, 7741, 12823, 19753, 21391, 22861, 28513, 36721, 37967, 40949, 60899, 76519, 83621, 101747, 121687, 127549, 128239, 142099, 149197, 153817, 155581, 158489, 160159, 169283, 173651, 180749, 185831, 192037, 198221

Offset: 1

David W. Wilson

nonn

Primes p such that 10*p+9, 100*p+99, 1000*p+999 and 10000*p+9999 are also primes. - Vincenzo Librandi, Aug 04 2010

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

Subsequence of A023240, A023270, A023301, and A102700.

[n: n in [1..5000000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999) and IsPrime(10000*n+9999)]; // Vincenzo Librandi, Aug 04 2010

Select[Prime[Range[20000]],AllTrue[Rest[NestList[10#+9&,#,4]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 16 2020 *)

a(n) == 9 or 13 (mod 14). - John Cerkan, Oct 09 2016

Definition clarified by Harvey P. Dale, Feb 16 2020

cp's OEIS Frontend

A023301 Primes that remain prime through 3 iterations of function f(x) = 10x + 9.

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