

A235481


Primes whose base4 representation is also the base9 representation of a prime.


3



2, 3, 29, 41, 61, 89, 109, 149, 157, 281, 293, 313, 401, 421, 433, 593, 701, 709, 1013, 1049, 1061, 1069, 1097, 1117, 1277, 1289, 1301, 1553, 1601, 1709, 2069, 2137, 2237, 2309, 2377, 2437, 2477, 2689, 2729, 2749, 2797, 2957, 2969, 3001, 3061, 3109, 3169, 3329, 3361, 3389, 3457, 3533, 3701
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OFFSET

1,1


COMMENTS

This sequence is part of a two dimensional array of sequences, given in the LINK, 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.
Appears to be a subsequence of A197636.


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime


EXAMPLE

29 = 131_4 and 131_9 = 109 are both prime, so 29 is a term.


MATHEMATICA

Select[Prime@Range@600, PrimeQ[FromDigits[IntegerDigits[#, 4], 9]] &] (* Giovanni Resta, Sep 12 2019 *)


PROG

(PARI) is(p, b=9, c=4)=isprime(vector(#d=digits(p, c), i, b^(#di))*d~)&&isprime(p) \\ Note: Code only valid for b > c.


CROSSREFS

Cf. A235473  A235480, A065720 ⊂ A036952, A065721  A065727, A089971 ⊂ A020449, A089981, A090707  A091924, A235394, A235395, A235461  A235482. See the LINK for further crossreferences.
Sequence in context: A141192 A215135 A059453 * A214889 A137472 A065932
Adjacent sequences: A235478 A235479 A235480 * A235482 A235483 A235484


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 12 2014


STATUS

approved



