A342810 Numbers k that divide the smallest number whose sum of digits is k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 27, 81, 191, 243, 729, 999, 2187, 2997, 6561, 8991, 19683, 26973, 33321, 36963, 39049, 59049, 80919, 100389, 110889, 118827, 177147, 177897, 183951, 242757, 332667, 356481, 531441, 551853, 728271, 998001, 1069443, 1367631, 1594323, 1655559, 2184813

Offset

1,2

Comments

By definition, if k divides A051885(k), then k is a term of this sequence.

From Ruediger Jehn, Jun 17 2021: (Start)

None of the terms is divisible by 2*5*11*13.

If a term x has the form 3^m * y where m > 1 (which is the case for the overwhelming number of terms of this sequence), then all prime factors of y are terms of A066364.

If a term x has the form 3^m * p * q where m > 1, where p is a term of A066364 and where q is the product of all other factors of the prime factorization of x, then all numbers 3^m * p^i * q are also terms for any integer i. (End)

Links

Kester Habermann, Table of n, a(n) for n = 1..792 (first 200 terms from Chai Wah Wu)

Rüdiger Jehn and Kester Habermann, Properties of terms of OEIS A342810, arXiv:2106.05866 [math.GM], 2021.

Example

21 is a term because the smallest number with a digital sum of 21 is 399 (A051885(21) = 399) which is divisible by 21.

Prog

(PARI) MAX=10000; for (e = 0, MAX, for (d = 1, 9, k =(d+1)*10^e - 1; x = d+9*e; if (k%x==0, print1(x, ", "); )))
(Python)
A342810_list = [n for n in range(1, 10**6) if n==1 or ((n % 9)+1)*pow(10, n//9, n) % n == 1] # Chai Wah Wu, Apr 04 2021

Crossrefs

Cf. A007953, A051885, A066364.

Sequence in context: A247813 A122639 A344748 * A086548 A083434 A305463

Adjacent sequences: A342807 A342808 A342809 * A342811 A342812 A342813

Keyword

nonn,base

Author

Ruediger Jehn, Mar 22 2021

Extensions

Name clarified by Jon E. Schoenfield, Apr 27 2021

Status

approved