A343924 a(n) = the maximum number of times n can be multiplied by a number > 1 such that each product has distinct digits.

15, 14, 10, 13, 10, 9, 6, 12, 5, 9, 3, 8, 6, 6, 10, 11, 3, 4, 5, 8, 5, 4, 6, 7, 3, 6, 10, 3, 4, 9, 4, 10, 3, 4, 5, 4, 4, 4, 6, 7, 3, 3, 2, 4, 4, 5, 2, 6, 5, 4, 8, 4, 3, 9, 3, 3, 3, 4, 4, 8, 3, 3, 3, 9, 4, 5, 4, 3, 4, 5, 3, 3, 4, 4, 4, 3, 4, 5, 5, 6, 4, 2, 3, 2, 4, 3, 3, 7, 5, 5, 4, 4, 2, 2, 4, 5

Offset

1,1

Comments

See A343925 for the list of numbers for each n which can multiply n to produce the maximum length series of products with distinct digits.

Links

Table of n, a(n) for n=1..96.

Formula

a(n) = 0 for n > 4938271605 or for any number n ending in two or more 0's.

Example

a(1) = 15 as 1 can be multiplied by 2 a total of fifteen times with each product containing distinct digits. The products are 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16348, 32768. No other number can multiply 1 to produce a longer series.
a(7) = 6 as 7 can be multiplied by 5 a total of six times with each product containing distinct digits. The products are 35, 175, 875, 4375, 21875, 109375. No other number can multiply 7 to produce a longer series.
a(17) = 3 as 17 can be multiplied by 2, 3, 6, or 17 a total of three times with each product containing distinct digits. For example for 17 the products are 289, 4913, 83521. No other numbers can multiply 17 to produce a longer series.

Crossrefs

Cf. A343925, A343921 (addition), A010784, A003991, A043537.

Sequence in context: A104056 A131285 A130677 * A022971 A023457 A004456

Adjacent sequences: A343921 A343922 A343923 * A343925 A343926 A343927

Keyword

nonn,base

Author

Scott R. Shannon, May 04 2021

Status

approved