A380435 Erase digit 0 from decimal expansion of n. Then repeatedly apply the number of divisor function (A000005) onto each digit until a stationary value is reached. a(n) is the final stationary value (if it is reached for all digits).

1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 11, 12, 12, 12, 12, 12, 12, 12, 12, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22, 22, 22, 22, 2, 21, 22, 22, 22, 22, 22

Offset

1,2

Comments

The number of iterations is 0, 1, 2, 3 for numbers containing the highest digits (1, 2), (3,5,7), (4, 9), (6, 8). n >= a(n) >= 1.

Links

Table of n, a(n) for n=1..76.

Formula

a(A007931(n)) = A007931(n).

For r = 1, k >= 0:

a(10^k) = 1

a((10^k - 1)/9) = (10^k - 1)/9.

For r from [2, 9], k >= 0:

a(r*10^k) = 2.

a(r*(10^k - 1)/9) = 2*(10^k - 1)/9.

Example

For n = 21 a(21) = 21.
For n = 408 we iterate 48 --> 34 --> 23 --> 22, thus, after 3 iterations, a(408) = 22.

Mathematica

a[n_] := FromDigits[IntegerDigits[n] /. {0 -> Nothing, _?(# > 1 &) -> 2}]; Array[a, 100] (* Amiram Eldar, Jan 24 2025 *)

Crossrefs

Cf. A002275, A002276 - A002283, A004719, A007931, A111066.

Sequence in context: A297035 A055178 A174847 * A215887 A159451 A378865

Adjacent sequences: A380432 A380433 A380434 * A380436 A380437 A380438

Keyword

nonn,base

Author

Ctibor O. Zizka, Jan 24 2025

Status

approved