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A181862 Decimal sturdy numbers: positive integers m such that sum of digits of k * m for any positive integer k is at least the sum of digits of m. 2
1, 3, 9, 10, 11, 12, 18, 21, 27, 30, 33, 36, 41, 45, 54, 63, 72, 81, 90, 99, 100, 101, 102, 108, 110, 111, 117, 120, 123, 126, 132, 135, 144, 153, 162, 171, 180, 198, 201, 207, 210, 216, 225, 231, 234, 243, 252, 261, 270, 297, 300, 303, 306, 315, 324, 330, 333, 342, 351, 360, 396, 405, 410 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Positive integers m such that A007953(m) = A077196(m).
All powers of 10 and many multiples of 3 are in this sequence, many prime numbers are not. Notable exceptions are the primes 11 and 41 that are in this sequence, and multiples of 3 like 6 and 15 that are not.
This suggests that a digit sum of 6 disqualifies a multiple of 3 from this sequence, not parity. A digit sum of 9, by contrast, ensures the number is in this sequence. - Alonso del Arte, Oct 02 2016
LINKS
Trevor Clokie, Thomas F. Lidbetter, Antonio Molina Lovett, Jeffrey Shallit, and Leon Witzman, Computational Aspects of Sturdy and Flimsy Numbers, arXiv:2002.02731 [cs.DS], 2020.
EXAMPLE
11 has a digit sum of 2. If a multiple of 11 exists with a digit sum of 1, that would mean a power of 10 is also a multiple of 11, which is absurd. Therefore 11 is in the sequence.
12 = 2^2 * 3 has a digit sum of 3. In base 10, all multiples of 3 have a digital root of 3, 6 or 9, which means that a total digit sum of 1 or 2 is impossible for a multiple of 3. Therefore 12 is in the sequence.
13 has a digit sum of 4. However, note that 7 * 11 * 13 = 1001, which has a digit sum of 2. So 13 is not in the sequence.
CROSSREFS
Sequence in context: A273893 A228165 A114022 * A329560 A330296 A043048
KEYWORD
nonn,base,changed
AUTHOR
Max Alekseyev, Nov 14 2010
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)