login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144753 Positive integers whose binary representation is a palindrome and has a prime number of 1's. 2
3, 5, 7, 9, 17, 21, 31, 33, 65, 73, 93, 107, 127, 129, 257, 273, 313, 341, 381, 403, 443, 471, 513, 1025, 1057, 1137, 1193, 1273, 1317, 1397, 1453, 1571, 1651, 1707, 1831, 2047, 2049, 4097, 4161, 4321, 4433, 4593, 4681, 4841, 4953, 5189, 5349, 5461, 5709 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Each term of this sequence is in both A006995 and A052294.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..11167 (terms 1..1000 from Vincenzo Librandi)
EXAMPLE
21 in binary is 10101. This binary representation is a palindrome, it contains three 1's, and three is a prime. So 21 is a term.
MATHEMATICA
okQ[n_] := Module[{idn2 = IntegerDigits[n, 2]}, (idn2 == Reverse[idn2]) && PrimeQ[First[DigitCount[n, 2]]]]; Select[Range[10000], okQ] (* Harvey P. Dale, Sep 23 2008 *)
PROG
(Python)
from sympy import isprime
def ok(n): b = bin(n)[2:]; return b == b[::-1] and isprime(b.count("1"))
print(list(filter(ok, range(5710)))) # 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("1"))
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(13)) # Michael S. Branicky, Sep 17 2021
CROSSREFS
Sequence in context: A146556 A084229 A191356 * A220221 A212292 A270837
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Sep 20 2008
EXTENSIONS
More terms from Harvey P. Dale, Sep 23 2008
Name edited by Michael S. Branicky, Sep 17 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)