A355377 Numbers k such that the concatenation of digits included in the sum and product of the digits of the number k is an anagram of the number k, and digits of the number are sorted in nondecreasing order.

119, 1236, 11359, 11449, 122669, 2334699, 13346899

Offset: 1

Author

Ilya Orlov, Jun 30 2022

Keywords

• nonn
• base
• fini
• full

Comments

From Michael S. Branicky, Jun 30 2022: (Start)

No more terms. [updated Jul 01 2022]

There are no terms > 10^87. If k is a d-digit number, Sum(digits(k)) <= 9*n, Product(digits(k)) <= 9^n, and d exceeds the sum of the number of digits in the latter two for d >= 88. (End)

a(n) is a digit permutation of A062237(n+9). - Thomas Scheuerle, Jun 30 2022

Examples

			11359 is a term since 1+1+3+5+9 = 19, 1*1*3*5*9 = 135, and 19135 is an anagram of 11359.
		

Crossrefs

Cf. A062237.

Programs

Python

import math
def is_ok(num):
    nums = [int(i) for i in str(num)]
    summa = sum(nums)
    prods = math.prod(nums)
    syms_1 = [str(i) for i in nums]
    syms_2 = [i for i in str(summa)] + [i for i in str(prods)]
    if syms_1 == sorted(syms_2):
        return True
    return False

Python

from math import prod
from itertools import count, islice, combinations_with_replacement as mc
def c(s):
    d = list(map(int, s))
    return sorted(s) == sorted(str(sum(d)) + str(prod(d)))
def ndgen(d): yield from ("".join(m) for m in mc("123456789", d))
def agen(): yield from (int(s) for d in count(1) for s in ndgen(d) if c(s))
print(list(islice(agen(), 7))) # Michael S. Branicky, Jun 30 2022