A057883
Smallest possible prime with at least n (from 2 to 10) distinct digits that remains prime (leading zeros not allowed) when all occurrences of its digits d are deleted.
Original entry on oeis.org
23, 137, 6173, 37019, 5600239, 476710937, 8192454631, 1645957688093, 78456580281239
Offset: 2
5600239 is a solution for at least 6 digits because 56239, 560039, 560029, 600239, 500239 and 560023 are all primes.
A057877
a(n) = smallest n-digit prime in A057876.
Original entry on oeis.org
23, 113, 1531, 12239, 111317, 1111219, 11119291, 111111197, 1111113173, 11111133017, 111111189919, 1111111411337, 11111111161177, 111111111263311, 1111111111149119, 11111111111179913, 111111111111118771, 1111111111111751371, 11111111111111111131, 111111111111113129773, 1111111111111111337111
Offset: 2
1531 gives primes 53, 131 and 151 after dropping digits 1, 5 and 3.
Cf.
A057876,
A057877,
A057878,
A057879,
A057880,
A057881,
A057882,
A057883,
A051362,
A034302,
A034303,
A034304,
A034305.
-
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:
Res:= NULL:
for t from 1 to 21 do
for x from (10^(t+1)-1)/9 by 2 do
if filter(x) then Res:= Res, x; break fi
od
od:
Res; # Robert Israel, Jul 13 2018
-
Do[k = (10^n - 1)/9; While[d = IntegerDigits[k]; !PrimeQ[k] || !PrimeQ[ FromDigits[ DeleteCases[d, 0]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 1]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 2]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 3]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 4]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 5]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 6]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 7]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 8]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 9]]], k++ ]; Print[k], {n, 2, 19}]
Showing 1-2 of 2 results.