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A372277
Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition, when written in binary.
0
87339, 332403, 9813039
OFFSET
1,1
COMMENTS
The base-2 version of A372046.
a(4) > 120000000000. - Robert P. P. McKone, May 20 2024
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
KEYWORD
nonn,base,bref,more
AUTHOR
Scott R. Shannon, Apr 25 2024
STATUS
approved