A179482
A subset of vampire numbers: n has a nontrivial factorization using n's digits in reverse order.
Original entry on oeis.org
126, 153, 688, 1395, 33579, 37668, 187029, 223524, 267034, 1008126, 1480368, 1514955, 1574253, 1766196, 1791495, 1831086, 1945944, 2784384, 10013323, 10353244, 18937617, 19437888, 23486976, 36528975, 38477586, 45334998, 48471696, 109019911, 116257833
Offset: 1
E.g. 126=6*21, 1395=5*9*31, 267034=4307*62.
A355973
Numbers that can be written as the product of two of its divisors such that the reverse of the binary value of the number equals the concatenation of the binary values of the divisors.
Original entry on oeis.org
351, 623, 5075, 5535, 21231, 69237, 78205, 88479, 89975, 101239, 173555, 286011, 339183, 357471, 625583, 687245, 1349487, 1415583, 2527343, 3094039, 5426415, 5648031, 5721183, 5764651, 6157723, 8512457, 10137575, 10974951, 11365839, 11775915, 14760911, 18617337, 21587823, 21734127, 22649247
Offset: 1
351 is a term as 351 = 101011111_2 = 3 * 117 = 11_2 * 1110101_2, and "101011111" in reverse is "111110101" which equals "11" + "1110101".
See the attached text file for other examples.
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Select[Range[2^18], Function[{k, d, m}, AnyTrue[Map[Join @@ IntegerDigits[#, 2] &, Transpose@ {d, k/d}], # == m &]] @@ {#, Divisors[#], Reverse@ IntegerDigits[#, 2]} &] (* Michael De Vlieger, Jul 23 2022 *)
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from sympy import divisors
def ok(n):
if not n&1: return False
t = bin(n)[2:][::-1]
return any(t==bin(d)[2:]+bin(n//d)[2:] for d in divisors(n, generator=True))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Apr 13 2024
A371666
Composite numbers which equal the reverse of the concatenation of their ascending ordered prime factors, with repetition, when written in binary.
Original entry on oeis.org
623, 78205, 101239, 80073085, 1473273719
Offset: 1
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.
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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<A371666_list = list(islice(A371666_gen(),3)) # Chai Wah Wu, Apr 13 2024
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