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

1,1

Links

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

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 *)

Prog

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

Crossrefs

A256186 is the intersection of this sequence with A000040.

Cf. A011540, A038618, A056709.

Sequence in context: A104048 A078499 A066027 * A142342 A008444 A268984

Adjacent sequences: A256224 A256225 A256226 * A256228 A256229 A256230

Keyword

nonn,base

Author

Charles R Greathouse IV and Zak Seidov, Mar 19 2015

Status

approved