A241020 a(n) is the smallest j such that the n-digit number consisting of a 1 in position j and 7's in the other n-1 positions is a prime, or 0 if no such prime exists.

1, 0, 1, 2, 0, 0, 6, 0, 1, 2, 0, 2, 1, 0, 3, 0, 0, 5, 2, 0, 6, 4, 0, 7, 4, 0, 12, 0, 0, 19, 8, 0, 26, 5, 0, 0, 33, 0, 6, 11, 0, 1, 23, 0, 18, 34, 0, 15, 0, 0, 1, 22, 0, 1, 50, 0, 32, 15, 0, 15, 25, 0, 21, 10, 0, 29, 47, 0, 0, 11, 0, 56, 14, 0, 2, 0, 0, 54, 3

Offset: 2

Author

Michel Lagneau, Apr 15 2014

Keywords

• nonn
• base

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) = 7 for i <> j. The sequence lists the smallest index j such that p is prime, or 0 if no such prime exists.

Except 0, the corresponding primes are 17, 0, 1777, 71777, 0, 0, 77777177, 0, 1777777777, 71777777777, 0, 7177777777777, 17777777777777, 0, 7717777777777777, 0, 0, 7777177777777777777, ... .

Links

• Robert Israel, Table of n, a(n) for n = 2..4000

Crossrefs

Cf. A241018, A241019.

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]:=7:
     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]:=7:
         fi:
         od:
          if ii=0
           then
           printf(`%d, `,0):
           else
          fi:
       od:

Mathematica

Flatten[Position[IntegerDigits[#],1]&/@Table[Select[FromDigits/@Permutations[ Join[ {1},PadRight[ {},n,7]]],PrimeQ]/.{}->{0,0},{n,80}][[;;,1]]/.{}->0] (* Harvey P. Dale, Jul 21 2024 *)

Python

from sympy import isprime
def a(n):
    if (1+7*(n-1))%3 == 0:
        return 0
    base = (10**n-1)//9*7
    for j in range(1, n+1):
        t = base - 6*10**(n-j)
        if isprime(t):
            return j
    return 0
print([a(n) for n in range(2, 81)]) # Michael S. Branicky, Jun 02 2024

Formula

a(n) = 0 when 7*(n-1) + 1 mod 3 = 0. - Michael S. Branicky, Jun 02 2024

Extensions

Name simplified by Michael S. Branicky, Jun 02 2024