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

1,1

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

Links

Table of n, a(n) for n=1..7.

Example

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

Prog

(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

Crossrefs

Cf. A062237.

Sequence in context: A373541 A126563 A362320 * A067134 A156930 A263128

Adjacent sequences: A355374 A355375 A355376 * A355378 A355379 A355380

Keyword

nonn,base,fini,full

Author

Ilya Orlov, Jun 30 2022

Status

approved