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A138148
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Cyclops numbers with binary digits only.
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102
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0, 101, 11011, 1110111, 111101111, 11111011111, 1111110111111, 111111101111111, 11111111011111111, 1111111110111111111, 111111111101111111111, 11111111111011111111111, 1111111111110111111111111, 111111111111101111111111111, 11111111111111011111111111111
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OFFSET
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0,2
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COMMENTS
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All members are palindromes A002113. The first five members are mentioned in A129868.
Also, binary representation of A129868.
a(A090748(n)) is equal to A138831(n), the n-th perfect number minus 1, written in base 2.
Except for the first term (replace 0 with 1) the binary representation of the n-th iteration of the elementary cellular automaton, Rule 219 starting with a single ON (black) cell. - Robert Price, Feb 21 2016
a(1) = 101 is only prime number in this sequence since a(n) = (10^(n+1)+1)*(10^n-1)/9. - Altug Alkan, May 11 2016
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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LINKS
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FORMULA
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a(n) = (-1-9*10^n+10^(1+2*n))/9.
G.f.: x*(200*x-101) / ((x-1)*(10*x-1)*(100*x-1)). (End)
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2. - Wesley Ivan Hurt, Dec 08 2015
E.g.f.: (-1 - 9*exp(9*x) + 10*exp(99*x))*exp(x)/9. - Ilya Gutkovskiy, May 12 2016
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EXAMPLE
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n ........ a(n) .... A129868(n): value of a(n) read in base 2.
0 ......... 0 ......... 0
1 ........ 101 ........ 5
2 ....... 11011 ....... 27
3 ...... 1110111 ...... 119
4 ..... 111101111 ..... 495
5 .... 11111011111 .... 2015
6 ... 1111110111111 ... 8127
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MAPLE
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MATHEMATICA
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Table[(-1 - 9*10^n + 10^(1 + 2*n))/9, {n, 0, 15}] (* Wesley Ivan Hurt, Dec 08 2015 *)
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PROG
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(PARI) for(n=1, 20, if(n%2==1, c=((10^n-1)/9)-10^((n-1)/2); print1(c, ", "))) \\ Felix Fröhlich, Jul 07 2014
(Magma) [(-1 - 9*10^n + 10^(1 + 2*n))/9 : n in [0..15]]; // Wesley Ivan Hurt, Dec 08 2015
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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