cp's OEIS Frontend

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.

%I A241020 #24 Jul 21 2024 11:12:36
%S A241020 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,
%T A241020 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,
%U A241020 0,21,10,0,29,47,0,0,11,0,56,14,0,2,0,0,54,3
%N 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.
%C A241020 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.
%C A241020 Except 0, the corresponding primes are 17, 0, 1777, 71777, 0, 0, 77777177, 0, 1777777777, 71777777777, 0, 7177777777777, 17777777777777, 0, 7717777777777777, 0, 0, 7777177777777777777, ... .
%H A241020 Robert Israel, <a href="/A241020/b241020.txt">Table of n, a(n) for n = 2..4000</a>
%F A241020 a(n) = 0 when 7*(n-1) + 1 mod 3 = 0. - _Michael S. Branicky_, Jun 02 2024
%p A241020 with(numtheory):nn:=80:T:=array(1..nn):
%p A241020    for n from 2 to nn do:
%p A241020      for i from 1 to n do:
%p A241020      T[i]:=7:
%p A241020      od:
%p A241020        ii:=0:
%p A241020        for j from 1 to n while(ii=0)do:
%p A241020        T[j]:=1:s:=sum('T[i]*10^(n-i)', 'i'=1..n):
%p A241020          if type(s,prime)=true
%p A241020          then
%p A241020          ii:=1: printf(`%d, `,j):
%p A241020          else
%p A241020          T[j]:=7:
%p A241020          fi:
%p A241020          od:
%p A241020           if ii=0
%p A241020            then
%p A241020            printf(`%d, `,0):
%p A241020            else
%p A241020           fi:
%p A241020        od:
%t A241020 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 *)
%o A241020 (Python)
%o A241020 from sympy import isprime
%o A241020 def a(n):
%o A241020     if (1+7*(n-1))%3 == 0:
%o A241020         return 0
%o A241020     base = (10**n-1)//9*7
%o A241020     for j in range(1, n+1):
%o A241020         t = base - 6*10**(n-j)
%o A241020         if isprime(t):
%o A241020             return j
%o A241020     return 0
%o A241020 print([a(n) for n in range(2, 81)]) # _Michael S. Branicky_, Jun 02 2024
%Y A241020 Cf. A241018, A241019.
%K A241020 nonn,base
%O A241020 2,4
%A A241020 _Michel Lagneau_, Apr 15 2014
%E A241020 Name simplified by _Michael S. Branicky_, Jun 02 2024