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.

19, 199, 1999, 99991, 199999, 9999991, 19999999, 0, 9199999999, 99999199999, 991999999999, 9919999999999, 99999999991999, 919999999999999, 9999999999999199, 99919999999999999, 0, 9991999999999999999, 99999199999999999999, 0, 9991999999999999999999

Offset: 2

Author

Michel Lagneau, Apr 15 2014

Keywords

• nonn
• base

Comments

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).

Links

• Michel Lagneau, Table of n, a(n) for n = 2..150

Crossrefs

Cf. A241018, A241019, A241020, A241022, A041027.

Programs

Maple

with(numtheory):nn:=80:T:=array(1..nn):
   for n from 2 to nn do:
     for i from 1 to n do:
     T[i]:=9:
     od:
       ii:=0:
       for j from 1 to n while(ii=0)do:
       T[j]:=1:s:=sum('T[i]*10^(n-i)', 'i'=1..n):
         if type(s,prime)=true
         then
         ii:=1: printf(`%d, `,s):
         else
         T[j]:=9:
         fi:
         od:
          if ii=0
           then
           printf(`%d, `,0):
           else
          fi:
     od:

Mathematica

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 *)