Search: id:A075442
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%I A075442
%S A075442 2,3,7,43,1811,654149,27082315109,153694141992520880899,
%T A075442 337110658273917297268061074384231117039,
%U A075442 8424197597064114319193772925959967322398440121059128471513803869133407474043
%N A075442 Slowest-growing sequence of primes whose reciprocals sum to 1.
%C A075442 This sequence was mentioned by K. S. Brown. The sequence is generated 
               by a greedy algorithm given by the Mathematica program. The sum converges 
               quadratically.
%C A075442 It is easily shown that this sequence is infinite. For suppose there 
               was a finite representation of unity as a sum of unit fractions with 
               distinct prime denominators. Multiply the equation by the product 
               of all denominators to obtain this product of prime numbers on one 
               side of the equation and a sum of products consisting of this product 
               with always exactly one of the prime numbers removed on the other 
               side. Then each of the prime numbers divides one side of the equation 
               but not the other, since it divides all the products added except 
               exactly one. Contradiction. - Peter C. Heinig (algorithms(AT)gmx.de), 
               Sep 22 2006
%D A075442 R. K. Guy, Unsolved Problems in Number Theory, D11.
%H A075442 K. S. Brown, <a href="http://www.mathpages.com/home/kmath454.htm">Odd, 
               Greedy and Stubborn (Unit Fractions)</a>
%H A075442 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EgyptianFraction.html">Egyptian Fraction</a>
%t A075442 x=1; lst={}; Do[n=Ceiling[1/x]; If[PrimeQ[n], n++ ]; While[ !PrimeQ[n], 
               n++ ]; x=x-1/n; AppendTo[lst, n], {10}]; lst
%Y A075442 Cf. A000058.
%Y A075442 Sequence in context: A072713 A129871 A000058 this_sequence A082993 A071580 
               A014546
%Y A075442 Adjacent sequences: A075439 A075440 A075441 this_sequence A075443 A075444 
               A075445
%K A075442 nice,nonn
%O A075442 1,1
%A A075442 T. D. Noe (noe(AT)sspectra.com), Sep 16 2002

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