A080790 - OEIS

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

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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