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Search: id:A134328
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| A134328 |
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The index n being written a1a2a3.....ak in base 10 for any vector P{p1,p2,p3,....pk)where p1<p2<p3<.....<pk are primes, A(P,n)=(p1^a1)*p2^a2)*(p3^a3)*.....(pk^ak) and B(P,n)= concatenation od primes and powers = p1&a1&p2&a2&p3&a3&.......&pk&ak. c(n) is the smallest number A(P,n) such as A(P,n)>B(p,n)if exists, else 0. |
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+0
2
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| 0, 121, 125, 625, 32, 64, 128, 256, 512, 0, 0, 219122, 24344, 4802, 6250, 31250, 4374, 13122, 39366, 0, 10170397, 24964, 8575, 2500, 12500, 2916, 8748, 26244, 78732, 31855013, 118459, 6125, 2744, 5000, 25000, 5832, 17496, 52488, 157464, 279841
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Computing the number of digits of A and B, it's easy to prove that for any n written only with 0 and 1, there is no solution, hence c(n) =0 It's the same for some other numbers n as 201,210,211,300,. . . . Any number of the submitted sequence c(n) of numbers A(P,n) satisfying the condition defines univocally and the number n and the vector P.On the contrary it should be not pertinent to submit the sequence of the associated numbers B(P,n) as the value of such a number does not define always univocally n and P. For example for n=26, c(n)=2916=(2^2)*(3^6) and B({2;3},26)=2236 which should be also be associated with A=223^6, as 223 is prime
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EXAMPLE
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for any p of q digits, p^1 contains q digits, but p&1 contains q+1 digits, hence c(1)=0
for p1 = 2,3,5 and 7, p1^2<p1&2 but 11^2=121<112, hence c(2)=121
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CROSSREFS
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Sequence in context: A137850 A036231 A055468 this_sequence A113614 A134941 A044867
Adjacent sequences: A134325 A134326 A134327 this_sequence A134329 A134330 A134331
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KEYWORD
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hard,nonn,uned
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)orange.fr), Jan 16 2008
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