login
A100459
Values of n for which the decimal number 10...090...01 is an n-digit prime.
3
3, 11, 143, 623
OFFSET
1,1
COMMENTS
a(5) > 84309. - Robert Price, Apr 14 2013
The number n must be of the form 2x+3, by definition. If x is odd, the number 10...090...01 is divisible by 11. Also, if x == 2 mod 6, it is divisible by 7. Thus, it must be either 4 mod 6 or 0 mod 6. Thus, 2*(6x+4) + 3 = 12x + 11 and 2*(6x+0) + 3 = 12x + 3, implying that a(n) must be congruent to 11 mod 12 or 3 mod 12. - Derek Orr, Jul 28 2014
EXAMPLE
10000900001 is an 11-digit prime. Thus 11 is a member of this sequence. - Derek Orr, Jul 27 2014
MATHEMATICA
2Select[Range[1000], PrimeQ[100^# + 9 * 10^# + 1] &] + 1 (* Alonso del Arte, Jul 28 2014 *)
PROG
(PARI)
for(n=0, 10^5, p=10^(2*n+2)+9*10^(n+1)+1; if(ispseudoprime(p), print1(2*n+3, ", "))) \\ Derek Orr, Jul 27 2014
CROSSREFS
Sequence in context: A329626 A072639 A201000 * A010682 A080987 A132561
KEYWORD
nonn,base,more,hard
AUTHOR
Harvey Dubner (harvey(AT)dubner.com), Nov 23 2004
STATUS
approved