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URL: https://oeis.org/A256227

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A256227
Naught-y numbers (A011540) that after removing all zeros become zeroless primes (A038618).
2
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
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.
Sequence in context: A104048 A078499 A066027 * A142342 A008444 A268984
KEYWORD
nonn,base
AUTHOR
STATUS
approved