OFFSET
1,1
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
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