A371666 Composite numbers which equal the reverse of the concatenation of their ascending ordered prime factors, with repetition, when written in binary.

623, 78205, 101239, 80073085, 1473273719

Offset

1,1

Comments

A subsequence of A355973. The first five numbers each have only two prime factors - do terms exist with three or more?

Links

Table of n, a(n) for n=1..5.

Example

101239 is a term as 101239_10 = 29_10 * 3491_10 = 11101_2 * 110110100011_2 = "11101110110100011"_2 which when reversed is "11000101101110111"_2 = 101239_10.

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A371666_gen(startvalue=4): # generator of terms >= startvalue
    for n in count(max(startvalue, 4)):
        f = factorint(n)
        if sum(f.values()) > 1:
            c = 0
            for p in sorted(f, reverse=True):
                a, q = p.bit_length(), int(bin(p)[:1:-1], 2)
                for _ in range(f[p]):
                    c = (c<<a)+q
            if c == n:
                yield n
A371666_list = list(islice(A371666_gen(), 3)) # Chai Wah Wu, Apr 13 2024

Crossrefs

Cf. A355973, A371821, A027750, A009944.

Sequence in context: A330932 A255086 A158373 * A265119 A283898 A345546

Adjacent sequences: A371663 A371664 A371665 * A371667 A371668 A371669

Keyword

nonn,base,more

Author

Scott R. Shannon, Apr 02 2024

Status

approved