A342034 a(n) is the number of numbers k with n digits where k has digits in nondecreasing order and satisfies k < (product of digits of k) * (sum of digits of k).

8, 41, 140, 367, 789, 1432, 2276, 3280, 4326, 5350, 6254, 7009, 7588, 7970, 8175, 8210, 8120, 7923, 7633, 7272, 6877, 6445, 6013, 5555, 5122, 4693, 4298, 3901, 3534, 3189, 2872, 2562, 2285, 2029, 1789, 1576, 1376, 1194, 1037, 893, 759, 654, 548, 454, 384, 315, 254, 210, 168, 127, 97, 79, 56, 39, 31, 21, 12, 8, 4

Offset

1,1

Comments

As A066310 is finite there exists m such that a(n) = 0 for all n > m.

a(n) = 0 for n >= 85 since 9^n*9n <= 10^(n-1) for n >= 85. This may occur as early as n = 60, as 9^n*9n <= 10^n-1 for n >= 60. But a(59) > 0 since 10^59-1 < 9^59*9*59. - Michael S. Branicky, Mar 05 2021

Links

Table of n, a(n) for n=1..59.

David A. Corneth, PARI program

Example

a(1) = 8 as there are 8 one-digit numbers k as described in name. Those are {2, 3, 4, 5, 6, 7, 8, 9}.

Prog

(Python)
from math import prod
from itertools import combinations_with_replacement as cwr
def c(digs): return int("".join(map(str, digs))) < prod(digs) * sum(digs)
def a(n): return sum(1 for u in cwr(range(1, 10), n) if c(u))
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Mar 05 2021
(PARI) See PARI link

Crossrefs

Cf. A009994, A066310.

Sequence in context: A250322 A135797 A171714 * A304160 A133106 A358588

Adjacent sequences: A342031 A342032 A342033 * A342035 A342036 A342037

Keyword

nonn,easy,base

Author

David A. Corneth, Mar 05 2021

Extensions

a(27)-a(41) from Michael S. Branicky, Mar 05 2021

Status

approved