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A057876
Primes p with the following property: let d_1, d_2, ... be the distinct digits occurring in the decimal expansion of p. Then for each d_i, dropping all the digits d_i from p produces a prime number. Leading 0's are not allowed.
10
23, 37, 53, 73, 113, 131, 137, 151, 173, 179, 197, 211, 311, 317, 431, 617, 719, 1531, 1831, 1997, 2113, 2131, 2237, 2273, 2297, 2311, 2797, 3137, 3371, 4337, 4373, 4733, 4919, 6173, 7297, 7331, 7573, 7873, 8191, 8311, 8831, 8837, 12239, 16673, 19531
OFFSET
1,1
LINKS
EXAMPLE
1531 gives primes 53, 131 and 151 after dropping digits 1, 5 and 3.
A larger example 1210778071 gives primes 12177871, 2077807, 110778071, 1210801 and 121077071 after dropping digits 0, 1, 2, 7 and 8.
MAPLE
filter:= proc(n) local L, d, Lp;
if not isprime(n) then return false fi;
L:= convert(n, base, 10);
for d in convert(L, set) do
Lp:= subs(d=NULL, L);
if Lp=[] or Lp[-1] = 0 then return false fi;
if not isprime(add(Lp[i]*10^(i-1), i=1..nops(Lp))) then return false fi;
od;
true
end proc:
select(filter, [seq(i, i=13..20000, 2)]); # Robert Israel, Jul 13 2018
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Oct 15 2000
EXTENSIONS
Name edited by Robert Israel, Jul 13 2018
STATUS
approved