A065721 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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