A335401 a(n) is the smallest positive number such that the decimal digits of n*a(n) are all 0, 1, 2 or 3.

1, 1, 1, 3, 2, 2, 3, 4, 37, 1, 1, 1, 1, 8, 2, 2, 6, 74, 7, 1, 1, 1, 1, 5, 4, 5, 49, 4, 7, 1, 1, 1, 1, 3, 6, 37, 3, 29, 8, 3, 3, 5, 7, 3, 74, 5, 26, 25, 27, 2, 2, 6, 4, 43, 2, 2, 23, 4, 17, 2, 2, 5, 21, 5, 2, 2, 3, 15, 19, 3, 3, 31, 14, 3, 4, 132, 3, 4, 27, 4, 41

Offset

1,4

Comments

If a(n) = k, then a(10n) = k.

a(n) = 1 iff n is in A007090; hence, except for a(1) = a(2) = a(3) = 1, the terms 1 always appear in strings of 4 consecutive 1's.

Records occur for n: 1, 4, 8, 9, 18, 76, ...

Links

Table of n, a(n) for n=1..81.

Formula

a(n) = A334914(n)/n.

Example

a(9)= 37 because 9*37=333 is the smallest multiple of 9 whose decimal digits are all 0, 1, 2 or 3.

Mathematica

a[n_] := Block[{k = 1}, While[Max@ IntegerDigits[k n] > 3, k++]; k]; Array[a, 81] (* Giovanni Resta, Jun 06 2020 *)

Prog

(PARI) a(n) = my(k=1); while(vecmax(digits(k*n))>3, k++); k; \\ Michel Marcus, Jun 08 2020

Crossrefs

Cf. A007090, A334914.

Cf. A079339 (similar, with digits 0 and 1), A181061 (similar, with digits 0, 1 and 2).

Sequence in context: A222456 A222673 A222666 * A324465 A361565 A334592

Adjacent sequences: A335398 A335399 A335400 * A335402 A335403 A335404

Keyword

nonn,base

Author

Bernard Schott, Jun 06 2020

Extensions

More terms from Giovanni Resta, Jun 06 2020

Status

approved