A066310 -id:A066310 - cp's OEIS frontend

A342227 Number of anagrams of A342226(n) in A066310.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 1, 2, 2, 3, 4, 1, 2, 4, 4, 2, 6, 6, 3, 6, 3, 1, 2, 2, 2, 2, 4, 4, 4, 4, 1, 3, 4

Offset: 1

David A. Corneth, Mar 06 2021

			A342226(275) = 2267. Its anagrams are 2267, 2276, 2627, 2672, 2726, 2762, 6227, 6272, 6722, 7226, 7262, 7622. Six of those are in A066310 (as they are less than (2 + 2 + 6 + 7) * (2 * 2 * 6 * 7) = 2856; the sum of digits times the product of digits, an invariant for anagrams). Those six numbers are the smallest six anagrams namely (2267, 2276, 2627, 2672, 2726, 2762).

Cf. A066310.

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).

Original entry on oeis.org

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

David A. Corneth, Mar 05 2021

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

			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}.

David A. Corneth, PARI program

Cf. A009994, A066310.

PARI
```
See PARI link
```

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

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

A342226 Numbers k with digits in nondecreasing order and satisfying k < (product of digits of k) * (sum of digits of k).

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 127, 128, 129, 136, 137, 138, 139, 145, 146, 147, 148, 149, 155, 156, 157, 158

Offset: 1

David A. Corneth, Mar 06 2021

This sequence contains 165623 terms.

			39 is in the sequence as 39 has digits in nondecreasing order and 39 < (3 + 9) * (3*9).

Intersection of A009994 and A066310.

cp's OEIS Frontend

A342227 Number of anagrams of A342226(n) in A066310.

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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).

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A342226 Numbers k with digits in nondecreasing order and satisfying k < (product of digits of k) * (sum of digits of k).

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