A065727 Primes p such that the decimal expansion of its base-9 conversion is also prime.

2, 3, 5, 7, 37, 43, 61, 109, 127, 199, 271, 277, 379, 457, 487, 523, 541, 613, 619, 673, 727, 757, 883, 907, 919, 991, 997, 1033, 1117, 1249, 1447, 1483, 1531, 1549, 1567, 1627, 1693, 1699, 1747, 1753, 1987, 2053, 2161, 2221, 2287, 2341, 2347, 2437, 2473

Offset: 1

Author

Patrick De Geest, Nov 15 2001

Keywords

• nonn
• base

Comments

In general rebase notation (Marc LeBrun): p9 = (9) [p] (10).

Examples

			E.g., 997_10 = 1327_9 is prime, and so is 1327_10.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A065720, A065721, A065722, A065723, A065724, A065725, A065726, A065361.

Intersection of A000040 and A036964.

Programs

Mathematica

Select[ Range[2500], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 9]]] & ]
NestList[NestWhile[NextPrime, #, ! PrimeQ[FromDigits[IntegerDigits[#2, 9]]] &, 2] &, 2, 48] (* Jan Mangaldan, Jul 01 2020 *)
Select[Prime[Range[400]],PrimeQ[FromDigits[IntegerDigits[#,9],10]]&] (* Harvey P. Dale, Sep 19 2021 *)

PARI

isok(p) = isprime(p) && isprime(fromdigits(digits(p, 9))); \\ Michel Marcus, Jul 02 2020