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

1,1

Comments

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

Example

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

Mathematica

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

Prog

(PARI) baseE(x, b)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 3); if (isprime(b), write("b065721.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 27 2009
(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

Crossrefs

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

Sequence in context: A107993 A131604 A139861 * A030472 A106998 A275114

Adjacent sequences: A065718 A065719 A065720 * A065722 A065723 A065724

Keyword

nonn,base

Author

Patrick De Geest, Nov 15 2001

Extensions

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

Status

approved