%I #31 Apr 20 2024 10:02:00

%S 3,11,41,101

%N 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.

%C Prime elements of A181862.

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

%C Contains prime repunits A004022 as a subsequence.

%C a(5) > 1.4*10^7. - _Giovanni Resta_, Sep 18 2018

%C From _Jason Yuen_, Mar 25 2024: (Start)

%C 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.

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

%H Trevor Clokie, Thomas F. Lidbetter, Antonio Molina Lovett, Jeffrey Shallit, and Leon Witzman, <a href="https://doi.org/10.1016/j.tcs.2022.05.029">Computational Aspects of Sturdy and Flimsy Numbers</a>, Theoretical Computer Science, Vol. 927 (2022), pp. 65-86; <a href="https://arxiv.org/abs/2002.02731">arXiv preprint</a>, arXiv:2002.02731 [cs.DS], 2020.

%H Jason Yuen, <a href="/A181863/a181863.txt">a181863_2e11.txt</a>. This file shows that a(5) > 2*10^11.

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

%K nonn,base,more,hard

%O 1,1

%A _Max Alekseyev_, Nov 14 2010