A144752 Positive integers whose binary representation is a palindrome and has a prime number of 0's.

9, 17, 21, 45, 51, 65, 85, 93, 99, 107, 189, 219, 231, 257, 297, 325, 365, 381, 387, 427, 443, 455, 471, 765, 891, 951, 975, 1105, 1161, 1241, 1285, 1365, 1421, 1501, 1533, 1539, 1619, 1675, 1755, 1787, 1799, 1879, 1911, 1935, 1967, 3069, 3579, 3831, 3951

Offset

1,1

Comments

Each term of this sequence is in both sequence A006995 and sequence A144754.

Links

Indranil Ghosh, Table of n, a(n) for n = 1..11167

Example

17 in binary is 10001. This binary representation is a palindrome, it contains three 0's, and three is a prime. So 17 is a term.

Prog

(Python)
from sympy import isprime
def ok(n): b = bin(n)[2:]; return b == b[::-1] and isprime(b.count('0'))
print(list(filter(ok, range(4000)))) # Michael S. Branicky, Sep 17 2021
(Python) # faster for computing initial segment of sequence
from sympy import isprime
from itertools import product
def ok2(bin_str): return isprime(bin_str.count("0"))
def bin_pals(maxdigits):
    yield from "01"
    digits, midrange = 2, [[""], ["0", "1"]]
    for digits in range(2, maxdigits+1):
        for p in product("01", repeat=digits//2-1):
            left = "1"+"".join(p)
            for middle in midrange[digits%2]:
                yield left + middle + left[::-1]
def auptopow2(e): return [int(b, 2) for b in filter(ok2, bin_pals(e))]
print(auptopow2(12)) # Michael S. Branicky, Sep 17 2021

Crossrefs

Cf. A144753, A006995, A144754

Sequence in context: A192049 A133246 A190151 * A317332 A073160 A242987

Adjacent sequences: A144749 A144750 A144751 * A144753 A144754 A144755

Keyword

base,nonn

Author

Leroy Quet, Sep 20 2008

Extensions

Extended by Ray Chandler, Nov 04 2008

Name edited by Michael S. Branicky, Sep 17 2021

Status

approved