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.

35, 333, 335, 445, 33445, 334445, 3333335, 3334445, 3444445, 33333445, 333333335, 334444445, 3333333335, 33333334445, 333333333335, 33333333334445, 33333333444445, 444444444444445, 333333334444444445, 333334444444444445, 444444444444444445, 3333333333333444445

Offset: 1

Author

Chai Wah Wu, Apr 26 2024

Keywords

• nonn
• base

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.

Examples

			   35 = 5*7
  333 = 3*3*37
  335 = 5*67
  445 = 5*89
33445 = 5*6689
333333333333333333333333444444444444444444444445 = 5*66666666666666666666666688888888888888888888889
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..71

Crossrefs

Cf. A372053, A372055, A372034, A372029.

Programs

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))