cp's OEIS Frontend

A372295 Composite numbers k such that k's prime factors are distinct, the digits of k are in nonincreasing order while the digits of the concatenation of k's ascending order prime factors are in nondecreasing order.

%I A372295 #28 Apr 27 2024 15:36:28
%S A372295 6,10,21,30,42,70,74,94,111,210,222,553,554,611,851,871,885,998,5530,
%T A372295 5554,7751,8441,8655,9998,85511,95554,99998,9999998,77744411,
%U A372295 5555555554,7777752221,8666666655,755555555554,95555555555554,999999999999998,5555555555555554,8666666666666655,755555555555555554
%N A372295 Composite numbers k such that k's prime factors are distinct, the digits of k are in nonincreasing order while the digits of the concatenation of k's ascending order prime factors are in nondecreasing order.
%C A372295 A number 999...9998 will be a term if it has two prime factors 2 and 4999...999. Therefore 999999999999998 and 999...9998 (with 54 9's) are both terms. See A056712.
%C A372295 The next term is greater than 10^11.
%H A372295 Michael S. Branicky, <a href="/A372295/b372295.txt">Table of n, a(n) for n = 1..40</a>
%e A372295 77744411 is a term as 77744411 = 233 * 333667 which has distinct prime factors, 77744411 has nonincreasing digits while its prime factor concatenation "233333667" has nondecreasing digits.
%o A372295 (Python)
%o A372295 from sympy import factorint, isprime
%o A372295 from itertools import count, islice, combinations_with_replacement as mc
%o A372295 def nd(s): return s == "".join(sorted(s))
%o A372295 def bgen(d):
%o A372295     yield from ("".join(m) for m in mc("9876543210", d) if m[0]!="0")
%o A372295 def agen(): # generator of terms
%o A372295     for d in count(1):
%o A372295         out = set()
%o A372295         for s in bgen(d):
%o A372295             t = int(s)
%o A372295             if t < 4 or isprime(t): continue
%o A372295             f = factorint(t)
%o A372295             if len(f) < sum(f.values()): continue
%o A372295             if nd("".join(str(p) for p in f)):
%o A372295                 out.add(t)
%o A372295         yield from sorted(out)
%o A372295 print(list(islice(agen(), 29))) # _Michael S. Branicky_, Apr 26 2024
%Y A372295 Cf. A372308, A372280, A056712, A372034, A372029, A372055, A027746, A372249.
%K A372295 nonn,base
%O A372295 1,1
%A A372295 _Scott R. Shannon_, Apr 25 2024
%E A372295 a(33)-a(38) from _Michael S. Branicky_, Apr 26 2024