

A235624


Primes whose base4 representation is also the base6 representation of a prime.


2



2, 3, 5, 13, 17, 37, 61, 73, 109, 157, 173, 181, 229, 233, 241, 257, 317, 337, 349, 373, 397, 409, 541, 557, 569, 601, 613, 661, 761, 769, 797, 821, 857, 953, 1013, 1021, 1033, 1069, 1153, 1181, 1193, 1201, 1229, 1237, 1297, 1321, 1373, 1429, 1481, 1609, 1621, 1637, 1709, 1801, 1861, 1877, 1889, 1901, 1973
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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.


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

5 = 11_4 and 11_6 = 7 are both prime, so 5 is a term.


MATHEMATICA

Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 4], 6] &] (* Giovanni Resta, Sep 12 2019 *)


PROG

(PARI) is(p, b=6, c=4)=isprime(vector(#d=digits(p, c), i, b^(#di))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.


CROSSREFS

Cf. A235616, A235265, A235266, A152079, A235461  A235482, A065720  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924, A235615  A235639. See the LINK for further crossreferences.
Sequence in context: A066111 A065820 A163268 * A108562 A087523 A073919
Adjacent sequences: A235621 A235622 A235623 * A235625 A235626 A235627


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 13 2014


STATUS

approved



