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

2,1

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

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 *)

Crossrefs

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

Sequence in context: A185687 A067272 A065582 * A055558 A160452 A113596

Adjacent sequences: A241018 A241019 A241020 * A241022 A241023 A241024

Keyword

nonn,base

Author

Michel Lagneau, Apr 15 2014

Status

approved