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Search: id:A137923
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| A137923 |
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Numbers whose digits are solutions of a Diophantine equation. |
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+0
3
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| 2, 3, 5, 7, 11, 12, 13, 15, 16, 18, 19, 21, 23, 25, 27, 29, 31, 32, 34, 35, 37, 43, 45, 51, 52, 53, 54, 56, 57, 58, 59, 61, 65, 72, 73, 75, 78, 79, 81, 85, 87, 89, 91, 92, 95, 97, 98
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Members of the sequence are numbers n = X(1)...X(r) ; for which digits the following Diophantine equation holds : [X(1)+...+X(r)] + [X(1)*X(2)+...X(r-1)*X(r)] +...+ [X(1)*...*X(r)] = p p is a prime number, X(i) digit of n; X(i) is from <1;9>.
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EXAMPLE
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2-digit numbers are in the form X(1)X(2).
The equation is then : X(1)+X(2)+ X(1)*X(2)= p ;
p prime, X(i) is from <1;9>. Power set is {();(1);(2);(1,2)}, so indices of digits in the equation are running thru the power set.
Following numbers n are solutions of the equation :
11 because 1+1+1*1 = 3
12;21 because 1+2+1*2 = 5
13;31 because 1+3+1*3 = 7
15;51 because 1+5+1*5 = 11
16;61 because 1+6+1*6 = 13
18;81 because 1+8+1*8 = 17
19;91 because 1+9+1*9 = 19
23;32 because 2+3+2*3 = 11
25;52 because 2+5+2*5 = 17
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CROSSREFS
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Sequence in context: A104193 A117288 A117283 this_sequence A163753 A131930 A001742
Adjacent sequences: A137920 A137921 A137922 this_sequence A137924 A137925 A137926
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KEYWORD
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easy,nonn,base
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AUTHOR
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Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Apr 30 2008
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