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

20, 30, 50, 70, 101, 103, 107, 109, 110, 130, 170, 190, 200, 203, 209, 230, 290, 300, 301, 307, 310, 370, 401, 403, 407, 410, 430, 470, 500, 503, 509, 530, 590, 601, 607, 610, 670, 700, 701, 703, 709, 710, 730, 790, 803, 809, 830, 890, 907, 970, 1001, 1003, 1007, 1009, 1010, 1013, 1027, 1030

Offset: 1

Author

Charles R Greathouse IV and Zak Seidov, Mar 19 2015

Keywords

• nonn
• base

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

A256186 is the intersection of this sequence with A000040.

Cf. A011540, A038618, A056709.

Programs

Maple

N:= 4: # to produce all terms with <= N digits
ZLO:= proc(d) # produce set of d-digit odd zeroless numbers
       option remember;
       if d = 1 then {1,3,5,7,9}
       else
         map(t -> seq(t+x*10^(d-1),x=1..9), ZLO(d-1))
       fi
end proc:
addzeros:= proc(x,d) # d-digit numbers formed by inserting 0's into x
        local L,n,R;
      L:= convert(x,base,10);
      n:= nops(L);
      R:= map(t -> [op(t),d], combinat[choose](d-1,n-1));
      seq(add(L[i]*10^(r[i]-1),i=1..n), r = R);
    end proc:
Z[1]:= {2,3,5,7}:
for i from 2 to N-1 do Z[i]:= select(isprime,ZLO(i)) od:
`union`(seq(seq(map(addzeros,Z[i],d), i=1..d-1),d=2..N));
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%,list)); # Robert Israel, Mar 19 2015

Mathematica

ss={};Do[id=IntegerDigits[p];If[Min[id]<1&&PrimeQ[FromDigits[Delete[id,Position[id,0]]]],ss={ss,p}],{p,20,2000}];Flatten[ss]
Select[Range[1200],DigitCount[#,10,0]>0&&PrimeQ[FromDigits[DeleteCases[ IntegerDigits[ #],0]]]&] (* Harvey P. Dale, Jan 01 2024 *)

PARI

is(n)=my(d=digits(n),e=select(x->x,d)); #e<#d && isprime(fromdigits(e)) \\ Charles R Greathouse IV, Mar 19 2015