

A235461


Primes whose base4 representation also is the base 2representation of a prime.


63



5, 17, 257, 277, 337, 1093, 1109, 1297, 1361, 4357, 5189, 16453, 16657, 16661, 17489, 17669, 17681, 17749, 21521, 21569, 21589, 65537, 65557, 65617, 65809, 66821, 70657, 70981, 70997, 81937, 82241, 83221, 83269, 86017, 86357, 87317
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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.
For further motivation and crossreferences, see sequence A235265 which is the main entry for this whole family of sequences.
When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=4, thus a subsequence of A077718 and therefore also of A000695, the Moserde Bruijn sequence.


LINKS

Table of n, a(n) for n=1..36.
M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime


EXAMPLE

5 = 11_4 and 11_2 = 3 are both prime, so 5 is a term.
17 = 101_4 and 101_2 = 5 are both prime, so 17 is a term.


PROG

(PARI) is(p, b=2, c=4)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#di))*d~)&&isprime(p)


CROSSREFS

Cf. A090707  A091924, A235462  A235482. See the LINK for further crossreferences.
Sequence in context: A191500 A089894 A077718 * A271660 A273948 A271657
Adjacent sequences: A235458 A235459 A235460 * A235462 A235463 A235464


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jan 11 2014


STATUS

approved



