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A348317 a(n) = A348150(n) - A002275(n) where A002275(n) = R_n is the repunit with n times digit 1. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 05:57 EST 2023. Contains 359837 sequences. (Running on oeis4.)