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A256227
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Naught-y numbers (A011540) that after removing all zeros become zeroless primes (A038618).
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2
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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
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listen;
history;
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internal format)
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OFFSET
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1,1
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LINKS
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) is(n)=my(d=digits(n), e=select(x->x, d)); #e<#d && isprime(fromdigits(e)) \\ Charles R Greathouse IV, Mar 19 2015
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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