Search: id:A121719
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%I A121719
%S A121719 4,6,8,9,20,22,24,26,28,30,33,36,39,40,42,44,46,48,50,55,60,62,63,64,66,
%T A121719 68,69,70,77,80,82,84,86,88,90,93,96,99,100,110,112,114,116,118,120,121,
%U A121719 130,132,134,136,138,140,143,144
%N A121719 Strings of digits which are composite regardless of the base in which 
               they are interpreted. Exclude bases in which numbers are not interpretable.
%C A121719 Comments from Franklin T. Adams-Watters:
%C A121719 "Think of these as polynomials. E.g. 121 is the polynomial n^2+2n+1. 
               There are three cases:
%C A121719 "(1) If the coefficients (digits) all have a common factor, the result 
               will be divisible by that factor.
%C A121719 "(2) If the polynomial can be factored, the numbers will be composite. 
               n^2+2n+1 = (n+1)^2, so it is always composite.
%C A121719 "(3) Otherwise, look at the polynomial modulo primes up to its degree. 
               For example, 112 (n^2+n+2, degree 2) modulo 2 is always 0, so it 
               is always divisible by 2.
%C A121719 "Note that condition (1) is really a special case of condition (2), where 
               one of the factors is a constant.
%C A121719 "If none of the above conditions apply, the polynomial will (probably) 
               have prime values."
%e A121719 String 55 in every base in which it is interpretable is divisible by 
               5. String 1001 in base a is divisible by a+1. Hence 55 and 1001 both 
               belong to this sequence.
%Y A121719 Sequence in context: A123710 A075243 A024370 this_sequence A162738 A161600 
               A032350
%Y A121719 Adjacent sequences: A121716 A121717 A121718 this_sequence A121720 A121721 
               A121722
%K A121719 more,nonn
%O A121719 1,1
%A A121719 Tanya Khovanova (tanyakh(AT)yahoo.com), Sep 08 2006
%E A121719 More terms from Franklin T. Adams-Watters, Sep 12 2006

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