

A231474


Primes whose base3 representation is also the base5 representation of a prime.


3



2, 3, 5, 7, 13, 17, 29, 31, 37, 41, 59, 67, 79, 97, 101, 109, 113, 137, 139, 149, 151, 173, 181, 193, 223, 229, 251, 269, 271, 293, 311, 331, 353, 367, 373, 379, 383, 389, 397, 401, 457, 467, 491, 503, 617, 631, 641, 647, 653, 673, 701, 773, 787, 797, 809, 829, 853, 857, 911, 929, 953, 977
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OFFSET

1,1


COMMENTS

This sequence is part of a twodimensional 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.


LINKS



EXAMPLE

7 = 21_3 and 21_5 = 11 are both prime, so 7 is a term.


MATHEMATICA

Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 3], 5] &] (* Giovanni Resta, Sep 12 2019 *)


PROG

(PARI) is(p, b=5, c=3)=isprime(vector(#d=digits(p, c), i, b^(#di))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.


CROSSREFS

Cf. A235265, A235266, A235473, A152079, A235461  A235482, A065720 ⊂ A036952, A065721  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924. See the LINK for further crossreferences.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



