

A235615


Primes whose base5 representation also is the base4 representation of a prime.


28



2, 3, 13, 41, 43, 61, 181, 191, 263, 281, 283, 331, 383, 431, 443, 463, 641, 643, 661, 881, 911, 1063, 1091, 1291, 1303, 1531, 1693, 2083, 2143, 2203, 2293, 2341, 3163, 3181, 3191, 3253, 3343, 3593, 3761, 3931, 4001, 4093, 4391, 4691, 4793, 5011, 5393, 5413, 5441, 6301
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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



EXAMPLE

Both 13 = 23_5 and 23_4 = 11 are prime.


PROG

(PARI) is(p, b=4, c=5)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#di))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 5, 4)&&print1(vector(#d=digits(p, 4), i, 5^(#di))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 5)


CROSSREFS

Cf. A235474, A235265, A235266, A152079, A235461  A235482, A065720  A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707  A091924, A235615  A235639. See the LINK for further crossreferences.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



