A372277 Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition, when written in binary.

87339, 332403, 9813039

Offset

1,1

Comments

The base-2 version of A372046.

a(4) > 120000000000. - Robert P. P. McKone, May 20 2024

Links

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

Example

332403 is a term as 332403 = 3 * 179 * 619 = 11_2 * 10110011_2 * 1001101011_2 = "11"_2 * "11001101"_2 * "1101011001"_2 when each prime factor is reversed. This gives "11110011011101011001"_2 when concatenated, and 11110011011101011001_2 = 997209 which is divisible by 332403.

Mathematica

a[n_Integer] := Module[{f}, f = Flatten[ConstantArray @@@ FactorInteger[n]]; If[Length[f] < 2, Return[False]]; Mod[FromDigits[StringJoin[StringReverse[IntegerString[#, 2]] & /@ f], 2], n] == 0];
Select[Range[2, 10^5], a] (* Robert P. P. McKone, May 02 2024 *)

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A372277_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):
                a = pow(2, len(s:=bin(p)[2:]), n)
                q = int(s[::-1], 2)
                for _ in range(f[p]):
                    c = (c*a+q)%n
            if not c:
                yield n
A372277_list = list(islice(A372277_gen(), 3)) # Chai Wah Wu, Apr 25 2024

Crossrefs

Cf. A372046, A371821, A371696, A027746.

Sequence in context: A237410 A206632 A230489 * A098186 A069313 A022207

Adjacent sequences: A372274 A372275 A372276 * A372278 A372279 A372280

Keyword

nonn,base,bref,more

Author

Scott R. Shannon, Apr 25 2024

Status

approved