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A090465
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.
4
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, 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, -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
OFFSET
1,4
COMMENTS
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.
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
LINKS
FORMULA
a(p) = 0 for p prime.
a(n) = -1 if n is a proper multiple of 3.
EXAMPLE
a(25) = 3 because three 9's must be appended to 25 before a prime is formed (25999).
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.
MAPLE
f:= proc(n) local x, m;
if n mod 3 = 0 and n <> 3 then return -1 fi;
x:= n;
for m from 0 to 10^4 do
if isprime(x) then return m fi;
x:= 10*x+9
od;
fail
end proc:
map(f, [$1..200]); # Robert Israel, Jun 05 2024
PROG
(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
CROSSREFS
Cf. A083747 (The Wilde Primes, i.e. same operation using ones), A090584 (using threes), A090464 (using sevens).
Sequence in context: A343030 A246690 A317748 * A364357 A052344 A339375
KEYWORD
base,sign
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Dec 02 2003
EXTENSIONS
Definition edited by M. F. Hasler, Jun 05 2024
STATUS
approved