A372277 - OEIS

%I #23 May 21 2024 05:34:24

%S 87339,332403,9813039

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

%C The base-2 version of A372046.

%C a(4) > 120000000000. - _Robert P. P. McKone_, May 20 2024

%e 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.

%t 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];

%t Select[Range[2, 10^5], a] (* _Robert P. P. McKone_, May 02 2024 *)

%o (Python)

%o from itertools import count, islice

%o from sympy import factorint

%o def A372277_gen(startvalue=4): # generator of terms >= startvalue

%o     for n in count(max(startvalue,4)):

%o         f = factorint(n)

%o         if sum(f.values()) > 1:

%o             c = 0

%o             for p in sorted(f):

%o                 a = pow(2,len(s:=bin(p)[2:]),n)

%o                 q = int(s[::-1],2)

%o                 for _ in range(f[p]):

%o                     c = (c*a+q)%n

%o             if not c:

%o                 yield n

%o A372277_list = list(islice(A372277_gen(),3)) # _Chai Wah Wu_, Apr 25 2024

%Y Cf. A372046, A371821, A371696, A027746.

%K nonn,base,bref,more

%O 1,1

%A _Scott R. Shannon_, Apr 25 2024