A080790 - OEIS

%I #13 Jul 30 2022 12:06:18

%S 11,13,23,29,37,41,43,47,53,61,67,71,83,97,101,113,131,151,163,167,

%T 173,181,193,197,199,223,227,229,233,251,263,269,277,283,307,331,337,

%U 349,353,359,373,383,409,421,431,433,449,461,463,479,487,491,503,509,521

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

%C Members of A074832 that are not in A006995. - _Robert Israel_, Aug 31 2016

%H Seiichi Manyama, <a href="/A080790/b080790.txt">Table of n, a(n) for n = 1..10000</a>

%e A000040(10)=29 -> '11101' rev '10111' -> 23=A000040(9), therefore 29 and 23 are terms.

%e 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.

%p revdigs:= proc(n) local L; L:= convert(n,base,2); add(L[-i]*2^(i-1),i=1..nops(L)) end proc:

%p filter:= proc(t) local r; if not isprime(t) then return false fi;

%p   r:= revdigs(t); r <> t and isprime(r) end proc:

%p select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Aug 30 2016

%o (Python)

%o from sympy import isprime

%o def ok(n):

%o     r = int(bin(n)[2:][::-1], 2)

%o     return n != r and isprime(n) and isprime(r)

%o print([k for k in range(600) if ok(k)]) # _Michael S. Branicky_, Jul 30 2022

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

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Mar 25 2003