

A235467


Primes whose base4 representation also is the base3 representation of a prime.


2



2, 89, 137, 149, 281, 293, 353, 389, 409, 421, 593, 613, 661, 1097, 1109, 1289, 1301, 1321, 1381, 1409, 1601, 1609, 1669, 2069, 2129, 2309, 2377, 2389, 2729, 4133, 4229, 4373, 4441, 4513, 4673, 5153
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OFFSET

1,1


COMMENTS

This sequence is part of the twodimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720  A065727, follow the same idea with one base equal to 10.
For further motivation and crossreferences, see sequence A235265 which is the main entry for this whole family of sequences.


LINKS



EXAMPLE

E.g., 89 = 1121_4 and 1121_3 = 43 both are prime.


MATHEMATICA

b4b3Q[n_]:=Module[{b4=IntegerDigits[n, 4]}, Max[b4]<3&&PrimeQ[ FromDigits[ b4, 3]]]; Select[Prime[Range[700]], b4b3Q] (* Harvey P. Dale, Dec 14 2021 *)


PROG

(PARI) is(p, b=3, c=4)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#di))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 4, 3)&&print1(vector(#d=digits(p, 3), i, 4^(#di))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 3, 4)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



