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
Examples
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.
Links
- Indranil Ghosh, Table of n, a(n) for n = 1..11167
Programs
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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
Extensions
Extended by Ray Chandler, Nov 04 2008
Name edited by Michael S. Branicky, Sep 17 2021
Comments