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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.
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%I #24 Jul 21 2024 11:12:36

%S 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 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 0,21,10,0,29,47,0,0,11,0,56,14,0,2,0,0,54,3

%N 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 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 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 Robert Israel, <a href="/A241020/b241020.txt">Table of n, a(n) for n = 2..4000</a>

%F a(n) = 0 when 7*(n-1) + 1 mod 3 = 0. - _Michael S. Branicky_, Jun 02 2024

%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]:=7:

%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]:=7:

%p fi:

%p od:

%p if ii=0

%p then

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

%p else

%p fi:

%p od:

%t 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 (Python)

%o from sympy import isprime

%o def a(n):

%o if (1+7*(n-1))%3 == 0:

%o return 0

%o base = (10**n-1)//9*7

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

%o t = base - 6*10**(n-j)

%o if isprime(t):

%o return j

%o return 0

%o print([a(n) for n in range(2, 81)]) # _Michael S. Branicky_, Jun 02 2024

%Y Cf. A241018, A241019.

%K nonn,base

%O 2,4

%A _Michel Lagneau_, Apr 15 2014

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