cp's OEIS Frontend

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

%I A372277 #23 May 21 2024 05:34:24
%S A372277 87339,332403,9813039
%N A372277 Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition, when written in binary.
%C A372277 The base-2 version of A372046.
%C A372277 a(4) > 120000000000. - _Robert P. P. McKone_, May 20 2024
%e A372277 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 A372277 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 A372277 Select[Range[2, 10^5], a] (* _Robert P. P. McKone_, May 02 2024 *)
%o A372277 (Python)
%o A372277 from itertools import count, islice
%o A372277 from sympy import factorint
%o A372277 def A372277_gen(startvalue=4): # generator of terms >= startvalue
%o A372277     for n in count(max(startvalue,4)):
%o A372277         f = factorint(n)
%o A372277         if sum(f.values()) > 1:
%o A372277             c = 0
%o A372277             for p in sorted(f):
%o A372277                 a = pow(2,len(s:=bin(p)[2:]),n)
%o A372277                 q = int(s[::-1],2)
%o A372277                 for _ in range(f[p]):
%o A372277                     c = (c*a+q)%n
%o A372277             if not c:
%o A372277                 yield n
%o A372277 A372277_list = list(islice(A372277_gen(),3)) # _Chai Wah Wu_, Apr 25 2024
%Y A372277 Cf. A372046, A371821, A371696, A027746.
%K A372277 nonn,base,bref,more
%O A372277 1,1
%A A372277 _Scott R. Shannon_, Apr 25 2024