A348792 Numbers k such that the reverse concatenation of the first k binary numbers A098780(k) is prime.

2, 3, 4, 7, 11, 13, 25, 97, 110, 1939

Offset: 1

Author

N. J. A. Sloane, Dec 03 2021

Keywords

• nonn
• base
• hard
• more

Examples

			a(4) = 7 is because the binary number 111 110 101 100 11 10 1 (with no spaces), which is 128413 in decimal, is prime.
		

Crossrefs

Cf. A000422, A007908, A098780, A176024.

Programs

Maple

q:= n-> isprime(Bits[Join](['Bits[Split](i)[]'$i=1..n])):
select(q, [$1..200])[];  # Alois P. Heinz, Dec 03 2021

Mathematica

f[n_] := FromDigits[Flatten @ IntegerDigits[Range[n, 1, -1], 2], 2]; Select[Range[120], PrimeQ[f[#]] &] (* Amiram Eldar, Dec 03 2021 *)

Python

from sympy import isprime
def afind(limit):
    s, k = "", 1
    for k in range(1, limit+1):
        s += bin(k)[2:][::-1]
        t = int(s[::-1], 2)
        if isprime(t):
            print(k, end=", ")
afind(200) # Michael S. Branicky, Dec 03 2021

Extensions

a(8)-a(10) from Amiram Eldar, Dec 03 2021