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a(n) = smallest n-digit prime in A057876.
2

%I #11 Jul 14 2018 02:48:31

%S 23,113,1531,12239,111317,1111219,11119291,111111197,1111113173,

%T 11111133017,111111189919,1111111411337,11111111161177,

%U 111111111263311,1111111111149119,11111111111179913,111111111111118771,1111111111111751371,11111111111111111131,111111111111113129773,1111111111111111337111

%N a(n) = smallest n-digit prime in A057876.

%e 1531 gives primes 53, 131 and 151 after dropping digits 1, 5 and 3.

%p filter:= proc(n) local L,d,Lp;

%p if not isprime(n) then return false fi;

%p L:= convert(n,base,10);

%p for d in convert(L,set) do

%p Lp:= subs(d=NULL,L);

%p if Lp=[] or Lp[-1] = 0 then return false fi;

%p if not isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp))) then return false fi;

%p od;

%p true

%p end proc:

%p Res:= NULL:

%p for t from 1 to 21 do

%p for x from (10^(t+1)-1)/9 by 2 do

%p if filter(x) then Res:= Res, x; break fi

%p od

%p od:

%p Res; # _Robert Israel_, Jul 13 2018

%t 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}]

%Y Cf. A057876, A057877, A057878, A057879, A057880, A057881, A057882, A057883, A051362, A034302, A034303, A034304, A034305.

%K base,nonn

%O 2,1

%A _Patrick De Geest_, Oct 15 2000

%E Extended by _Robert G. Wilson v_, Dec 17 2002

%E More terms from _Robert Israel_, Jul 13 2018