%I #20 Jun 06 2024 11:27:29

%S 1,0,0,2,0,-1,0,1,-1,1,0,-1,0,1,-1,2,0,-1,0,2,-1,1,0,-1,3,1,-1,4,0,-1,

%T 0,2,-1,1,1,-1,0,1,-1,1,0,-1,0,1,-1,16,0,-1,1,1,-1,3,0,-1,5,1,-1,15,0,

%U -1,0,2,-1,12,1,-1,0,2,-1,1,0,-1,0,2,-1,1,3,-1,0,1,-1,1,0,-1,1,2,-1,33,0,-1,1,1,-1,3,10,-1,0,3,-1,1,0,-1,0,1,-1,1,0,-1

%N Smallest number m such that (n+1)*10^m-1 (i.e., n with m nines appended) yields a prime, or -1 if this will always yield a composite number.

%C The first 9 record holders in this sequence are 1, 4, 25, 28, 46, 88, 374, 416, 466 with the values 1, 2, 3, 4, 16, 33, 57, 70, 203 respectively.

%C The next 3 record holders are 1342, 1802, 1934 with the values 29711, 45882, 51836 respectively. 4420 may be the next record holder as no solution has been found for it yet. 4420 was tested out to 300000 nines with no prime formed. - _Toshitaka Suzuki_, May 27 2024

%H Toshitaka Suzuki, <a href="/A090465/b090465.txt">Table of n, a(n) for n = 1..4419</a>

%F a(p) = 0 for p prime.

%F a(n) = -1 if n is a proper multiple of 3.

%e a(25) = 3 because three 9's must be appended to 25 before a prime is formed (25999).

%e a(6) = -1 because no matter how many 9's are appended to 6, the resulting number is always divisible by 3 and can therefore not be prime.

%p f:= proc(n) local x,m;

%p if n mod 3 = 0 and n <> 3 then return -1 fi;

%p x:= n;

%p for m from 0 to 10^4 do

%p if isprime(x) then return m fi;

%p x:= 10*x+9

%p od;

%p fail

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Jun 05 2024

%o (PARI) apply( {A090465(n, LIM=500)=n%3 && for(m=0, LIM, ispseudoprime(n) && return(m); n=n*10+9); -(n>3)}, [1..55]) \\ Retun value -1 means that a(n) = -1 or, if n%3 > 0, then possibly a(n) > LIM, the search limit given as second (optional) parameter. - _M. F. Hasler_, Jun 05 2024

%Y Cf. A083747 (The Wilde Primes, i.e. same operation using ones), A090584 (using threes), A090464 (using sevens).

%K base,sign

%O 1,4

%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 02 2003

%E Definition edited by _M. F. Hasler_, Jun 05 2024