A371821 Composite numbers which divide the concatenation of their ascending ordered prime factors, with repetition, when written in binary.

85329, 177904587, 333577497

Offset

1,1

Comments

The base 2 version of A259047. Assuming a(4) exists it is greater than 10^10.

a(4) <= 55133857902732922904331439521901. - Chai Wah Wu, Apr 12 2024

a(1), a(3), the bound on a(4) above, and larger terms can be generated using an adaptation of the method of J. K. Andersen referenced in A259047; see linked Python program for an implementation and two more terms. - Michael S. Branicky, Apr 12 2024

Links

Table of n, a(n) for n=1..3.

Michael S. Branicky, Python program generating terms in A371821

Example

177904587 is a term as 177904587 = 3_10 * 7_10 * 103_10 * 233_10 * 353_10 = 11_2 * 111_2 * 1100111_2 * 11101001_2 * 101100001_2 = "11111110011111101001101100001"_2 = 533713761_10, which is divisible by 177904587.

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A371821_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue, 1)):
        f = sorted(factorint(n, multiple=True))
        if len(f) > 1:
            c = 0
            for p in f:
                c = ((c<<p.bit_length())+p)%n
            if not c:
                yield n
A371821_list = list(islice(A371821_gen(), 3)) # Chai Wah Wu, Apr 11 2024
(Python)
from sympy import factorint, isprime
def ok(n): return not isprime(n) and int("".join(bin(p)[2:]*e for p, e in factorint(n).items()), 2)%n == 0 # Michael S. Branicky, Apr 12 2024

Crossrefs

Cf. A027746, A004676, A259047, A371641.

Sequence in context: A375263 A031671 A371641 * A010083 A235968 A195468

Adjacent sequences: A371818 A371819 A371820 * A371822 A371823 A371824

Keyword

nonn,base,more,bref

Author

Scott R. Shannon, Apr 07 2024

Status

approved