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A256227 Naught-y numbers (A011540) that after removing all zeros become zeroless primes (A038618).

%I A256227 #21 Jan 01 2024 12:24:02
%S A256227 20,30,50,70,101,103,107,109,110,130,170,190,200,203,209,230,290,300,
%T A256227 301,307,310,370,401,403,407,410,430,470,500,503,509,530,590,601,607,
%U A256227 610,670,700,701,703,709,710,730,790,803,809,830,890,907,970,1001,1003,1007,1009,1010,1013,1027,1030
%N A256227 Naught-y numbers (A011540) that after removing all zeros become zeroless primes (A038618).
%H A256227 Harvey P. Dale, <a href="/A256227/b256227.txt">Table of n, a(n) for n = 1..1000</a>
%p A256227 N:= 4: # to produce all terms with <= N digits
%p A256227 ZLO:= proc(d) # produce set of d-digit odd zeroless numbers
%p A256227        option remember;
%p A256227        if d = 1 then {1,3,5,7,9}
%p A256227        else
%p A256227          map(t -> seq(t+x*10^(d-1),x=1..9), ZLO(d-1))
%p A256227        fi
%p A256227 end proc:
%p A256227 addzeros:= proc(x,d) # d-digit numbers formed by inserting 0's into x
%p A256227         local L,n,R;
%p A256227       L:= convert(x,base,10);
%p A256227       n:= nops(L);
%p A256227       R:= map(t -> [op(t),d], combinat[choose](d-1,n-1));
%p A256227       seq(add(L[i]*10^(r[i]-1),i=1..n), r = R);
%p A256227     end proc:
%p A256227 Z[1]:= {2,3,5,7}:
%p A256227 for i from 2 to N-1 do Z[i]:= select(isprime,ZLO(i)) od:
%p A256227 `union`(seq(seq(map(addzeros,Z[i],d), i=1..d-1),d=2..N));
%p A256227 # if using Maple 11 or earlier, uncomment the next line
%p A256227 # sort(convert(%,list)); # _Robert Israel_, Mar 19 2015
%t A256227 ss={};Do[id=IntegerDigits[p];If[Min[id]<1&&PrimeQ[FromDigits[Delete[id,Position[id,0]]]],ss={ss,p}],{p,20,2000}];Flatten[ss]
%t A256227 Select[Range[1200],DigitCount[#,10,0]>0&&PrimeQ[FromDigits[DeleteCases[ IntegerDigits[ #],0]]]&] (* _Harvey P. Dale_, Jan 01 2024 *)
%o A256227 (PARI) is(n)=my(d=digits(n),e=select(x->x,d)); #e<#d && isprime(fromdigits(e)) \\ _Charles R Greathouse IV_, Mar 19 2015
%Y A256227 A256186 is the intersection of this sequence with A000040.
%Y A256227 Cf. A011540, A038618, A056709.
%K A256227 nonn,base
%O A256227 1,1
%A A256227 _Charles R Greathouse IV_ and _Zak Seidov_, Mar 19 2015