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A089981
Primes whose decimal representation also represents a prime in base 3.
73
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
1,1
COMMENTS
See A065721 for the primes given by these terms considered as numbers written in base 3, i.e., the sequence with the definition "working in the opposite sense". - M. F. Hasler, Jan 05 2014
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
Cf. A031974, A089971, A090707, A090708, A090709, A090710, A235394, A235395, A000040 and further references therein.
Sequence in context: A275002 A004813 A342294 * A368480 A365179 A028487
KEYWORD
base,nonn
AUTHOR
Cino Hilliard, Jan 18 2004
EXTENSIONS
Definition and example reworded, offset corrected and cross-references added by M. F. Hasler, Jan 05 2014
STATUS
approved