

A235639


Primes whose base9 representation is also the base6 representation of a prime.


27



2, 3, 5, 19, 23, 41, 113, 127, 131, 163, 199, 271, 419, 433, 739, 743, 761, 919, 991, 1009, 1013, 1063, 1153, 1171, 1459, 1481, 1499, 1553, 1567, 1571, 1733, 1747, 1783, 1873, 1913, 2237, 2377, 2381, 2539, 2557, 2593, 2633, 2939, 3011, 3079, 3083, 3187, 3259, 3331, 3659
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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.


LINKS

Robert Israel, 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

19 = 21_9 and 21_6 = 13 are both prime, so 19 is a term.
509 = 625_9 and 625_6 = 17 are both prime, but 625 is not a valid base6 integer, so 509 is not a term.


MAPLE

R:= 2: x:= 2: count:= 1:
while count < 100 do
x:= nextprime(x);
L:= convert(x, base, 6);
y:= add(9^(i1)*L[i], i=1..nops(L));
if isprime(y) then count:= count+1; R:= R, y fi
od:
R; # Robert Israel, May 18 2020


PROG

(PARI) is(p, b=6, c=9)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#di))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 9, 6)&&print1(vector(#d=digits(p, 6), i, 9^(#di))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 6, 9)


CROSSREFS

Cf. A231481, A235265, A235266, A152079, A235461  A235482, A065720  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924, A235615  A235638. See the LINK for further crossreferences.
Sequence in context: A019377 A215320 A215357 * A040107 A254670 A348900
Adjacent sequences: A235636 A235637 A235638 * A235640 A235641 A235642


KEYWORD

nonn,base,look


AUTHOR

M. F. Hasler, Jan 13 2014


STATUS

approved



