A241018 a(n) is the smallest j such that the n-digit number consisting of a 1 in position j and 9's in the other n-1 positions is a prime, or 0 if no such prime exists.

1, 1, 1, 5, 1, 7, 1, 0, 2, 6, 3, 3, 11, 2, 14, 4, 0, 4, 6, 0, 4, 20, 6, 7, 18, 1, 1, 23, 8, 8, 23, 7, 0, 0, 0, 26, 33, 0, 11, 8, 5, 8, 13, 12, 44, 2, 2, 0, 11, 31, 17, 39, 1, 51, 5, 7, 4, 29, 9, 16, 0, 0, 26, 14, 26, 10, 13, 0, 0, 34, 40, 0, 15, 3, 14, 32, 0

Offset

2,4

Comments

Previous name: Let x(1)x(2)...x(n) denote the decimal expansion of a number p having an index j such that x(j) = 1 and x(i) = 9 for i <> j. a(n) is the smallest index j such that p is prime, or 0 if no such prime exists.

Except 0, the corresponding primes are 19, 199, 1999, 99991, 199999, 9999991, 19999999, 0, 9199999999, 99999199999, 991999999999, 9919999999999, ... .

Links

Robert Israel, Table of n, a(n) for n = 2..4033

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, `, j):
         else
         T[j]:=9:
         fi:
         od:
          if ii=0
           then
           printf(`%d, `, 0):
           else
          fi:
       od:

Mathematica

Table[With[{w = ConstantArray[9, n]}, SelectFirst[Range@ n, PrimeQ@ FromDigits@ ReplacePart[w, # -> 1] &]] /. m_ /; MissingQ@ m -> 0, {n, 2, 78}] (* Michael De Vlieger, Sep 13 2017 *)

Prog

(Python)
from sympy import isprime
def a(n):
    base = (10**n-1)
    for j in range(1, n+1):
        t = base - 8*10**(n-j)
        if isprime(t):
            return j
    return 0
print([a(n) for n in range(2, 78)]) # Michael S. Branicky, Jun 02 2024

Crossrefs

Cf. A241019, A241020.

Sequence in context: A197733 A353874 A354052 * A348500 A308090 A300711

Adjacent sequences: A241015 A241016 A241017 * A241019 A241020 A241021

Keyword

nonn,base

Author

Michel Lagneau, Apr 15 2014

Extensions

Name simplified by Jon E. Schoenfield, Sep 13 2017

Status

approved