OFFSET
1,2
COMMENTS
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
Jason Yuen, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn,base
AUTHOR
Max Alekseyev, Nov 14 2010
STATUS
approved