A065721 Primes p whose base-3 expansion is also the decimal expansion of a prime.

2, 67, 79, 103, 139, 157, 181, 193, 199, 211, 229, 277, 283, 307, 313, 349, 367, 373, 409, 421, 433, 439, 463, 523, 541, 547, 571, 577, 751, 829, 883, 919, 1021, 1033, 1039, 1087, 1171, 1249, 1303, 1429, 1483, 1579, 1597, 1621, 1741, 1783, 1789, 1873

Offset: 1

Author

Patrick De Geest, Nov 15 2001

Keywords

• nonn
• base

Comments

In general rebase notation (Marc LeBrun): p3 = (3) [p] (10).

Examples

			1033_10 = 1102021_3 is prime, and so is 1102021_10.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Primes in A036954.

Cf. A065720 up to A065727, A065361. See the Links for further cross-references.

Programs

Mathematica

Select[ Range[1900], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 3]]] & ]

PARI

is(p,b=10,c=3)=isprime(vector(#c=digits(p,c),i,b^(#c-i))*c~)&&isprime(p) \\ M. F. Hasler, Jan 12 2014

Extensions

Definition clarified by M. F. Hasler, Jan 12 2014