A080790 Binary emirps, primes whose binary reversal is a different prime.

11, 13, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 83, 97, 101, 113, 131, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 251, 263, 269, 277, 283, 307, 331, 337, 349, 353, 359, 373, 383, 409, 421, 431, 433, 449, 461, 463, 479, 487, 491, 503, 509, 521

Offset: 1

Author

Reinhard Zumkeller, Mar 25 2003

Keywords

• nonn
• base

Comments

Members of A074832 that are not in A006995. - Robert Israel, Aug 31 2016

Examples

			A000040(10) = 29 -> '11101' rev '10111' -> 23 = A000040(9), therefore 29 and 23 are terms.
The prime 19 is not a term, as 19 -> '10011' rev '11001' -> 25 = 5^2; and 7 = A074832(3) is not a term because it is a binary palindrome (A006995) and therefore not different.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006567, A006995, A074832, A004676, A007088.

Programs

Maple

revdigs:= proc(n) local L; L:= convert(n,base,2); add(L[-i]*2^(i-1),i=1..nops(L)) end proc:
filter:= proc(t) local r; if not isprime(t) then return false fi;
  r:= revdigs(t); r <> t and isprime(r) end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Aug 30 2016

Mathematica

Select[Prime[Range[100]], (r = IntegerReverse[#, 2]) != # && PrimeQ[r] &] (* Amiram Eldar, Jul 28 2025 *)

Python

from sympy import isprime
def ok(n):
    r = int(bin(n)[2:][::-1], 2)
    return n != r and isprime(n) and isprime(r)
print([k for k in range(600) if ok(k)]) # Michael S. Branicky, Jul 30 2022