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A241021 Smallest prime numbers p of length n having a decimal expansion x(1)x(2)... x(n) such that there exists an index j where x(j) = 1 and x(i) = 9 for i<>j, or 0 if no such prime exists.

%I A241021 #17 Dec 10 2017 10:35:28
%S A241021 19,199,1999,99991,199999,9999991,19999999,0,9199999999,99999199999,
%T A241021 991999999999,9919999999999,99999999991999,919999999999999,
%U A241021 9999999999999199,99919999999999999,0,9991999999999999999,99999199999999999999,0,9991999999999999999999
%N A241021 Smallest prime numbers p of length n having a decimal expansion x(1)x(2)... x(n) such that there exists an index j where x(j) = 1 and x(i) = 9 for i<>j, or 0 if no such prime exists.
%C A241021 The corresponding indices of the decimal digit 1 are 1, 1, 1, 5, 1, 7, 1, 0, 2, 6, 3, 3, 11, 2, 14, 4, 0, 4, 6, 0, 4, ... (A241018).
%H A241021 Michel Lagneau, <a href="/A241021/b241021.txt">Table of n, a(n) for n = 2..150</a>
%p A241021 with(numtheory):nn:=80:T:=array(1..nn):
%p A241021    for n from 2 to nn do:
%p A241021      for i from 1 to n do:
%p A241021      T[i]:=9:
%p A241021      od:
%p A241021        ii:=0:
%p A241021        for j from 1 to n while(ii=0)do:
%p A241021        T[j]:=1:s:=sum('T[i]*10^(n-i)', 'i'=1..n):
%p A241021          if type(s,prime)=true
%p A241021          then
%p A241021          ii:=1: printf(`%d, `,s):
%p A241021          else
%p A241021          T[j]:=9:
%p A241021          fi:
%p A241021          od:
%p A241021           if ii=0
%p A241021            then
%p A241021            printf(`%d, `,0):
%p A241021            else
%p A241021           fi:
%p A241021      od:
%t A241021 Table[SelectFirst[FromDigits/@Table[Insert[PadRight[{},k,9],1,n],{n,k+1}],PrimeQ],{k,30}]/.Missing["NotFound"]->0 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 10 2017 *)
%Y A241021 Cf. A241018, A241019, A241020, A241022, A041027.
%K A241021 nonn,base
%O A241021 2,1
%A A241021 _Michel Lagneau_, Apr 15 2014