A348317 a(n) = A348150(n) - A002275(n) where A002275(n) = R_n is the repunit with n times digit 1.

0, 1, 0, 5, 1, 3, 1, 1, 0, 14, 1, 15, 5, 3, 3, 11, 1, 21, 8, 10, 6, 5, 1, 3, 2, 12, 0, 17, 25, 14, 5, 13, 6, 74, 1, 54, 41, 12, 8, 14, 4, 105, 41, 55, 63, 33, 25, 13, 5, 103, 3, 33, 40, 63, 3, 52, 15, 23, 40, 21, 20, 10, 21, 11, 25, 33, 41, 47, 45, 14, 1, 171

Offset

1,4

Comments

a(n) measures the gap between the smallest n-digit number not containing the digit 0 and the smallest n-digit Niven number not containing the digit 0.

For more informations and links, see A348150.

a(n) = 0 iff n is in A014950.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

a(n) = A348150(n) - A002275(n).

Example

A348150(4) = 1116 since it is the smallest 4-digit integer not containing the digit 0 that is divisible by the sum of its digits:1116 = (1+1+1+6) * 124;  A002275(4) = R_4 = 1111, hence a(4) = 1116 - 1111 = 5.

Mathematica

hQ[n_] := ! MemberQ[(d = IntegerDigits[n]), 0] && Divisible[n, Plus @@ d]; a[n_] := Module[{m= (10^n - 1)/9, k=0}, While[! hQ[m+k], k++]; k]; Array[a, 30] (* Amiram Eldar, Oct 13 2021 *)

Prog

(Python)
def a(n):
    s, k = "1"*n, int("1"*n)
    while '0' in s or k%sum(map(int, s)): k += 1; s = str(k)
    return k - int("1"*n)
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Oct 12 2021
(PARI) a(n) = my(r=(10^n-1)/9); for(k=r, 10^n-1, if (vecmin(digits(k)) && !(k % sumdigits(k)), return (k-r))); \\ Michel Marcus, Oct 13 2021

Crossrefs

Cf. A002275, A005349, A014950, A217973, A348150.

Sequence in context: A201526 A091384 A011305 * A254378 A134568 A198798

Adjacent sequences: A348314 A348315 A348316 * A348318 A348319 A348320

Keyword

nonn,base

Author

Bernard Schott, Oct 12 2021

Extensions

a(23) and beyond from Michael S. Branicky, Oct 12 2021

Status

approved