cp's OEIS Frontend

A241019 a(n) is the smallest j such that the n-digit number consisting of a 1 in position j and 3's in the other n-1 positions is a prime, or 0 if no such prime exists.

%I A241019 #15 Jun 04 2024 01:31:36
%S A241019 1,2,3,2,2,4,2,6,5,5,5,0,3,8,1,11,7,6,4,5,11,5,0,0,9,11,0,5,5,0,4,5,
%T A241019 17,19,19,6,0,3,9,35,1,27,24,32,0,36,14,11,34,14,22,0,17,53,0,47,11,0,
%U A241019 16,3,0,15,0,39,22,40,27,39,0,19,2,19,48,2,43,19
%N A241019 a(n) is the smallest j such that the n-digit number consisting of a 1 in position j and 3's in the other n-1 positions is a prime, or 0 if no such prime exists.
%C A241019 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) = 3 for i <> j.  The sequence lists the smallest index j such that p is prime, or 0 if no such prime exists.
%C A241019 Except 0, the corresponding primes are 13, 313, 3313, 31333, 313333, 3331333, 31333333, 333331333, 3333133333, 33331333333, 333313333333, 0, 33133333333333, ... .
%H A241019 Robert Israel, <a href="/A241019/b241019.txt">Table of n, a(n) for n = 2..4001</a>
%p A241019 with(numtheory):nn:=80:T:=array(1..nn):
%p A241019    for n from 2 to nn do:
%p A241019      for i from 1 to n do:
%p A241019      T[i]:=3:
%p A241019      od:
%p A241019        ii:=0:
%p A241019        for j from 1 to n while(ii=0)do:
%p A241019        T[j]:=1:s:=sum('T[i]*10^(n-i)', 'i'=1..n):
%p A241019          if type(s,prime)=true
%p A241019          then
%p A241019          ii:=1: printf(`%d, `,j):
%p A241019          else
%p A241019          T[j]:=3:
%p A241019          fi:
%p A241019          od:
%p A241019           if ii=0
%p A241019            then
%p A241019            printf(`%d, `,0):
%p A241019            else
%p A241019           fi:
%p A241019        od:
%o A241019 (Python)
%o A241019 from sympy import isprime
%o A241019 def a(n):
%o A241019     base = (10**n-1)//9*3
%o A241019     for j in range(1, n+1):
%o A241019         t = base - 2*10**(n-j)
%o A241019         if isprime(t):
%o A241019             return j
%o A241019     return 0
%o A241019 print([a(n) for n in range(2, 78)]) # _Michael S. Branicky_, Jun 02 2024
%Y A241019 Cf. A241018, A241020.
%K A241019 nonn,base
%O A241019 2,2
%A A241019 _Michel Lagneau_, Apr 15 2014
%E A241019 Name simplified and offset corrected by _Michael S. Branicky_, Jun 02 2024