cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A100459 Values of n for which the decimal number 10...090...01 is an n-digit prime.

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%I A100459 #20 Jul 29 2014 21:03:27
%S A100459 3,11,143,623
%N A100459 Values of n for which the decimal number 10...090...01 is an n-digit prime.
%C A100459 a(5) > 84309. - _Robert Price_, Apr 14 2013
%C A100459 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
%e A100459 10000900001 is an 11-digit prime. Thus 11 is a member of this sequence. - _Derek Orr_, Jul 27 2014
%t A100459 2Select[Range[1000], PrimeQ[100^# + 9 * 10^# + 1] &] + 1 (* _Alonso del Arte_, Jul 28 2014 *)
%o A100459 (PARI)
%o A100459 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
%Y A100459 Cf. A100028, A171553.
%K A100459 nonn,base,more,hard
%O A100459 1,1
%A A100459 Harvey Dubner (harvey(AT)dubner.com), Nov 23 2004