

A235615


Primes whose base 5 representation also is the base 4 representation of a prime.


27



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 two dimensional 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

Table of n, a(n) for n=1..50.
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime


EXAMPLE

E.g., 13 = 23[5] and 23[4] = 11 both 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.
Sequence in context: A289549 A259261 A141511 * A117528 A264042 A122719
Adjacent sequences: A235612 A235613 A235614 * A235616 A235617 A235618


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 13 2014


STATUS

approved



