OFFSET
1,1
COMMENTS
In general rebase notation (Marc LeBrun): p2 = (2) [p] (10).
Also: Primes in A036952. - M. F. Hasler, Dec 11 2012
See A089971 for the binary representation of these terms. - M. F. Hasler, Jan 05 2014
LINKS
Harry J. Smith and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
Carlos Rivera, Puzzle 280. 3893257, The Prime Puzzles & Problems Connection.
FORMULA
EXAMPLE
1009{10} = 1111110001{2} is prime, and 1111110001{10} is also prime.
89 is in the sequence because it is a prime. Binary representation of 89 = 1011001, which is also a prime.
MAPLE
select(t -> isprime(t) and isprime(convert(t, binary)), [seq(2*i+1, i=1..1000)]); # Robert Israel, Jul 08 2014
MATHEMATICA
Select[ Range[1900], PrimeQ[ # ] && PrimeQ[ FromDigits[ IntegerDigits[ #, 2]]] & ]
Select[ Prime@ Range@ 330, PrimeQ[ FromDigits[ IntegerDigits[#, 2]]] &] (* Robert G. Wilson v, Oct 09 2014 *)
PROG
(PARI) {(baseE(x, b)= local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); e); n=0; for (m=1, 10^9, p=prime(m); b=baseE(p, 2); if (isprime(b), write("b065720.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 27 2009
(PARI) isok(p) = isprime(p) && isprime(fromdigits(binary(p), 10)); \\ Michel Marcus, Mar 04 2022
(Python)
from sympy import isprime
def ok(n): return isprime(n) and isprime(int(bin(n)[2:]))
print([k for k in range(2100) if ok(k)]) # Michael S. Branicky, Mar 04 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Nov 15 2001
EXTENSIONS
a(48)-a(50) from K. D. Bajpai, Jul 04 2014
STATUS
approved