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A147757
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Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.
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6
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1, 11, 101, 1001, 10101, 101101, 1011101, 10111101, 101111101, 1011111101, 10111111101, 101111111101, 1011111111101, 10111111111101, 101111111111101, 1011111111111101, 10111111111111101, 101111111111111101
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OFFSET
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1,2
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COMMENTS
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a(n) is also A147758(n) written in base 2.
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LINKS
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FORMULA
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G.f.: x+11*x^2+101*x^3-91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ). - R. J. Mathar, Aug 24 2011
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EXAMPLE
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n .... Successive digits of a(n)
1 ............. ( 1 )
2 ............ ( 1 1 )
3 ........... ( 1 0 1 )
4 .......... ( 1 0 0 1 )
5 ......... ( 1 0 1 0 1 )
6 ........ ( 1 0 1 1 0 1 )
7 ....... ( 1 0 1 1 1 0 1 )
8 ...... ( 1 0 1 1 1 1 0 1 )
9 ..... ( 1 0 1 1 1 1 1 0 1 )
10 ... ( 1 0 1 1 1 1 1 1 0 1 )
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MATHEMATICA
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f[n_] := Block[{w = {1, 0}}, Which[n == 1, w = {1}, n == 2, w = {1, 1}, n == 3, AppendTo[w, 1], n >= 4, w = Join[w, Table[1, {n - 4}], Reverse@ w]]; FromDigits@ w]; Array[f, 19] (* Michael De Vlieger, Dec 05 2015 *)
LinearRecurrence[{11, -10}, {1, 11, 101, 1001, 10101}, 20] (* Harvey P. Dale, Aug 02 2017 *)
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PROG
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(PARI) Vec( x+11*x^2+101*x^3 -91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ) + O(x^30)) \\ Michel Marcus, Dec 05 2015
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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