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

2,4

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) = 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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A241018, A241019.

Sequence in context: A205974 A098643 A193474 * A277444 A274710 A028625

Adjacent sequences: A241017 A241018 A241019 * A241021 A241022 A241023

Keyword

nonn,base

Author

Michel Lagneau, Apr 15 2014

Extensions

Name simplified by Michael S. Branicky, Jun 02 2024

Status

approved