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A226019
Primes whose binary reversal is a square.
1
2, 19, 79, 149, 569, 587, 1237, 2129, 2153, 2237, 2459, 2549, 4129, 4591, 4657, 4999, 8369, 8999, 9587, 9629, 9857, 10061, 17401, 17659, 17737, 18691, 20149, 20479, 33161, 33347, 34631, 35117, 35447, 39023, 40427, 40709, 66403, 68539, 74707, 75703, 79063, 79333, 80071
OFFSET
1,1
COMMENTS
The sequence of corresponding squares begins: 1, 25, 121, 169, 625, 841, 1369, 2209, 2401, 3025, 3481, 2809, 4225, 7921, ...
For n>1 the second and third most significant bits of a(n) are "0" because all odd squares are equal to 1 mod 8. - Andres Cicuttin, May 12 2016
MATHEMATICA
Select[Table[Prime[j], {j, 1, 10000}], Element[Sqrt[FromDigits[Reverse[IntegerDigits[#, 2]], 2]], Integers]&] (* Andres Cicuttin, May 12 2016 *)
PROG
(Python)
import math
primes = []
def addPrime(k):
for p in primes:
if k%p==0: return
if p*p > k: break
primes.append(k)
r = 0
p = k
while k:
r = r*2 + (k&1)
k>>=1
s = int(math.sqrt(r))
if s*s == r: print(p, end=', ')
addPrime(2)
addPrime(3)
for i in range(5, 1000000000, 6):
addPrime(i)
addPrime(i+2)
(Python)
from sympy import isprime
A226019_list, i, j = [2], 0, 0
while j < 2**34:
p = int(format(j, 'b')[::-1], 2)
if j % 2 and isprime(p):
A226019_list.append(p)
j += 2*i+1
i += 1
A226019_list = sorted(A226019_list) # Chai Wah Wu, Dec 20 2015
(Python)
from sympy import integer_nthroot, primerange
def ok(p): return integer_nthroot(int(bin(p)[:1:-1], 2), 2)[1]
def aupto(lim): return [p for p in primerange(2, lim+1) if ok(p)]
print(aupto(80071)) # Michael S. Branicky, Feb 19 2021
(PARI) isok(k) = isprime(k) && issquare(fromdigits(Vecrev(binary(k)), 2)); \\ Michel Marcus, Feb 19 2021
CROSSREFS
Subsequence of A204219. Cf. also A235027.
Sequence in context: A256112 A272053 A317274 * A057326 A129446 A240280
KEYWORD
nonn,base,changed
AUTHOR
Alex Ratushnyak, May 23 2013
STATUS
approved