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Consider the difference (A033873(k)) between the smallest prime > 10^k and 10^k; sequence lists the successive values of A033873(k) which are primes.
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%I #9 May 03 2021 17:14:14

%S 7,3,3,19,7,7,19,3,37,31,37,61,3,3,7,13,67,103,331,61,193,67,43,3,109,

%T 31,193,151,31,3,19,7,79,13,103,151,373,181,31,79,97,151,127,3,3,79,3,

%U 19,457,7,139,271,79,709,79,3,283,7,283,13,13,73,67,13,151,37,193,337

%N Consider the difference (A033873(k)) between the smallest prime > 10^k and 10^k; sequence lists the successive values of A033873(k) which are primes.

%t f[n_]:=Module[{x=10^n},NextPrime[x]-x];Select[f/@Range[0,200],PrimeQ] (* _Harvey P. Dale_, May 03 2021 *)

%Y This is the prime subsequence of A033873. Cf. A033874.

%K nonn

%O 1,1

%A _Cino Hilliard_, Aug 27 2004

%E Definition corrected by _N. J. A. Sloane_, May 03 2021. Thanks to _Harvey P. Dale_ for pointing out that something was wrong.