A241019 - OEIS

%I #15 Jun 04 2024 01:31:36

%S 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 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 16,3,0,15,0,39,22,40,27,39,0,19,2,19,48,2,43,19

%N 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 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 Except 0, the corresponding primes are 13, 313, 3313, 31333, 313333, 3331333, 31333333, 333331333, 3333133333, 33331333333, 333313333333, 0, 33133333333333, ... .

%H Robert Israel, <a href="/A241019/b241019.txt">Table of n, a(n) for n = 2..4001</a>

%p with(numtheory):nn:=80:T:=array(1..nn):

%p    for n from 2 to nn do:

%p      for i from 1 to n do:

%p      T[i]:=3:

%p      od:

%p        ii:=0:

%p        for j from 1 to n while(ii=0)do:

%p        T[j]:=1:s:=sum('T[i]*10^(n-i)', 'i'=1..n):

%p          if type(s,prime)=true

%p          then

%p          ii:=1: printf(`%d, `,j):

%p          else

%p          T[j]:=3:

%p          fi:

%p          od:

%p           if ii=0

%p            then

%p            printf(`%d, `,0):

%p            else

%p           fi:

%p        od:

%o (Python)

%o from sympy import isprime

%o def a(n):

%o     base = (10**n-1)//9*3

%o     for j in range(1, n+1):

%o         t = base - 2*10**(n-j)

%o         if isprime(t):

%o             return j

%o     return 0

%o print([a(n) for n in range(2, 78)]) # _Michael S. Branicky_, Jun 02 2024

%Y Cf. A241018, A241020.

%K nonn,base

%O 2,2

%A _Michel Lagneau_, Apr 15 2014

%E Name simplified and offset corrected by _Michael S. Branicky_, Jun 02 2024