cp's OEIS Frontend

A372151 For a positive number k, let L(k) denote the list consisting of k followed by the prime factors of k, with repetition, in nondecreasing order; sequence gives composite k such that the digits of k is either 3, 4 or 5 and the digits of L(k) are in nondecreasing order.

%I A372151 #11 Apr 29 2024 09:30:15
%S A372151 35,333,335,445,33445,334445,3333335,3334445,3444445,33333445,
%T A372151 333333335,334444445,3333333335,33333334445,333333333335,
%U A372151 33333333334445,33333333444445,444444444444445,333333334444444445,333334444444444445,444444444444444445,3333333333333444445
%N A372151 For a positive number k, let L(k) denote the list consisting of k followed by the prime factors of k, with repetition, in nondecreasing order; sequence gives composite k such that the digits of k is either 3, 4 or 5 and the digits of L(k) are in nondecreasing order.
%C A372151 Subsequence of A372029. Sequence is inspired by the observation that most terms in A372029 so far contain only the digits 3, 4 and 5.
%H A372151 Chai Wah Wu, <a href="/A372151/b372151.txt">Table of n, a(n) for n = 1..71</a>
%e A372151    35 = 5*7
%e A372151   333 = 3*3*37
%e A372151   335 = 5*67
%e A372151   445 = 5*89
%e A372151 33445 = 5*6689
%e A372151 333333333333333333333333444444444444444444444445 = 5*66666666666666666666666688888888888888888888889
%o A372151 (Python)
%o A372151 from itertools import count, islice, combinations_with_replacement
%o A372151 from sympy import isprime, factorint
%o A372151 def A372151_gen(): # generator of terms
%o A372151     for l in count(1):
%o A372151         for d in combinations_with_replacement('345',l):
%o A372151             a, n = d[-1], int(''.join(d))
%o A372151             if not isprime(n):
%o A372151                 for p in factorint(n,multiple=True):
%o A372151                     s = str(p)
%o A372151                     if s[0] < a or sorted(s) != list(s):
%o A372151                         break
%o A372151                     a = s[-1]
%o A372151                 else:
%o A372151                     yield n
%o A372151 A372151_list = list(islice(A372151_gen(),20))
%Y A372151 Cf. A372053, A372055, A372034, A372029.
%K A372151 nonn,base
%O A372151 1,1
%A A372151 _Chai Wah Wu_, Apr 26 2024