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

1,1

Comments

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

Links

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

Example

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.

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

Prog

(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

Crossrefs

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

Sequence in context: A075519 A019406 A289688 * A066123 A370011 A048393

Adjacent sequences: A080787 A080788 A080789 * A080791 A080792 A080793

Keyword

nonn,base

Author

Reinhard Zumkeller, Mar 25 2003

Status

approved