

A235461


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


64



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, 263429, 263489, 267541, 278549
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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



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)
(Python)
from itertools import islice
from sympy import nextprime, isprime
def A235461_gen(): # generator of terms
p = 1
while (p:=nextprime(p)):
if isprime(m:=int(bin(p)[2:], 4)):
yield m


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



