A181863 Decimal sturdy primes: primes p such that sum of digits of k*p for any positive integer k is at least the sum of digits of p.

3, 11, 41, 101

Offset: 1

Author

Max Alekseyev, Nov 14 2010

Keywords

• nonn
• base
• more
• hard

Comments

Prime elements of A181862.

Primes p such that A007953(p) = A077196(p).

Contains prime repunits A004022 as a subsequence.

a(5) > 1.4*10^7. - Giovanni Resta, Sep 18 2018

From Jason Yuen, Mar 25 2024: (Start)

For all x>log_10(p), 1+A007953(p-(10^x mod p)) >= A007953(p). This follows from the fact that 10^x+p-(10^x mod p) is a multiple of p.

a(5) > 2*10^11. See a181863_2e11.txt for more details. (End)

Links

• Trevor Clokie, Thomas F. Lidbetter, Antonio Molina Lovett, Jeffrey Shallit, and Leon Witzman, Computational Aspects of Sturdy and Flimsy Numbers, Theoretical Computer Science, Vol. 927 (2022), pp. 65-86; arXiv preprint, arXiv:2002.02731 [cs.DS], 2020.
• Jason Yuen, a181863_2e11.txt. This file shows that a(5) > 2*10^11.

Crossrefs

Cf. A004022, A007953, A077196, A143027, A181862.