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A320587 Primes that are not Base-3 deletable primes (written in base 10).

%I A320587 #44 Dec 07 2018 12:27:09
%S A320587 3,13,31,37,41,43,67,79,97,103,109,113,127,131,139,149,151,157,163,
%T A320587 193,199,211,227,229,239,241,257,271,277,281,283,293,307,311,313,331,
%U A320587 337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,433,439,443
%N A320587 Primes that are not Base-3 deletable primes (written in base 10).
%C A320587 A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.
%C A320587 Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.
%C A320587 Complement of all primes and A319596.
%H A320587 Robert Price, <a href="/A320587/b320587.txt">Table of n, a(n) for n = 1..906</a>
%t A320587 b = 3; d = {};
%t A320587 p = Select[Range[2, 10000], PrimeQ[#] &];
%t A320587 For[i = 1, i <= Length[p], i++,
%t A320587   c = IntegerDigits[p[[i]], b];
%t A320587   If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
%t A320587   For[j = 1, j <= Length[c], j++,
%t A320587    t = Delete[c, j];
%t A320587    If[t[[1]] == 0, Continue[]];
%t A320587 If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]]; Complement[Table[Prime[n], {n, PrimePi[Last[d]]}], d] (* _Robert Price_, Dec 06 2018 *)
%Y A320587 Cf. A080608, A080603, A096235-A096246.
%K A320587 nonn,base,easy
%O A320587 1,1
%A A320587 _Robert Price_, Nov 14 2018
%E A320587 Added the term 3. As pointed out by Kevin Ryde, there is no need to "seed" the list using base-2 assumptions. - _Robert Price_, Dec 06 2018