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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.
1
35, 333, 335, 445, 33445, 334445, 3333335, 3334445, 3444445, 33333445, 333333335, 334444445, 3333333335, 33333334445, 333333333335, 33333333334445, 33333333444445, 444444444444445, 333333334444444445, 333334444444444445, 444444444444444445, 3333333333333444445
OFFSET
1,1
COMMENTS
Subsequence of A372029. Sequence is inspired by the observation that most terms in A372029 so far contain only the digits 3, 4 and 5.
LINKS
EXAMPLE
35 = 5*7
333 = 3*3*37
335 = 5*67
445 = 5*89
33445 = 5*6689
333333333333333333333333444444444444444444444445 = 5*66666666666666666666666688888888888888888888889
PROG
(Python)
from itertools import count, islice, combinations_with_replacement
from sympy import isprime, factorint
def A372151_gen(): # generator of terms
for l in count(1):
for d in combinations_with_replacement('345', l):
a, n = d[-1], int(''.join(d))
if not isprime(n):
for p in factorint(n, multiple=True):
s = str(p)
if s[0] < a or sorted(s) != list(s):
break
a = s[-1]
else:
yield n
A372151_list = list(islice(A372151_gen(), 20))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Chai Wah Wu, Apr 26 2024
STATUS
approved