A089981 Primes whose decimal representation also represents a prime in base 3.
2, 2111, 2221, 10211, 12011, 12211, 20201, 21011, 21101, 21211, 22111, 101021, 101111, 102101, 102121, 110221, 111121, 111211, 120011, 120121, 121001, 121021, 122011, 201101, 202001, 202021, 210011, 210101, 1000211, 1010201, 1012201
Offset: 1
Examples
2111 is a prime and its decimal representation is also a valid base-3 representation (because all digits are < 3), and 2111[3] = 67[10] is again a prime. Therefore 2111 is in the sequence.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
- Alejandro J. Becerra Jr., Python code for computing terms of A089971, A089981, A090707-A090710, A235394-A235395.
Crossrefs
Programs
-
Mathematica
Select[ FromDigits@# & /@ IntegerDigits[ Prime@ Range@ 270, 3], PrimeQ] (* Robert G. Wilson v, Jan 05 2014 *) FromDigits/@Select[Tuples[{0,1,2},7],AllTrue[{FromDigits[#],FromDigits[ #,3]},PrimeQ]&] (* Harvey P. Dale, Aug 15 2022 *)
-
PARI
is_A089981(p)=vecmax(d=digits(p))<3&&isprime(vector(#d,i,3^(#d-i))*d~)&&isprime(p) \\ "d" is implicitly declared local. Putting isprime(p) to the end improves performance when the function is applied to primes only, as below, or to very large numbers. - M. F. Hasler, Jan 05 2014
-
PARI
forprime(p=2,1e6,is_A089981(p)&&print1(p",")) \\ - M. F. Hasler, Jan 05 2014
-
PARI
fixBase(n, oldBase, newBase)=my(d=digits(n, oldBase), t=newBase-1); for(i=1, #d, if(d[i]>t, for(j=i, #d, d[j]=t); break)); fromdigits(d, newBase) list(lim)=my(v=List(), t); forprime(p=2, fixBase(lim\1, 10, 3), if(isprime(t=fromdigits(digits(p, 3), 10)), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Nov 07 2016
Extensions
Definition and example reworded, offset corrected and cross-references added by M. F. Hasler, Jan 05 2014
Comments