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 A135577 Numbers that have only the digit "1" as first, central and final digit. For numbers with 5 or more digits the rest of digits are "0". 13
 1, 111, 10101, 1001001, 100010001, 10000100001, 1000001000001, 100000010000001, 10000000100000001, 1000000001000000001, 100000000010000000001, 10000000000100000000001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, equal to A135576(n), written in base 2. Essentially the same as A066138. - R. J. Mathar Apr 29 2008 a(n) has 2n-1 digits. LINKS G. C. Greubel, Table of n, a(n) for n = 1..500 Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000). FORMULA a(n) = A135576(n), written in base 2. Also, a(1)=1, for n>1; a(n)=(concatenation of 1, n-2 digits 0, 1, n-2 digits 0 and 1). a(n) = 10^(2*n-2) + 10^(n-1) + 1 - 2*(C(2*(n-1),n-1) mod 2). - Paolo P. Lava, Nov 26 2008 From Colin Barker, Sep 16 2013: (Start) a(n) = 1 + 10^(n-1) + 100^(n-1) for n>1. a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>4. G.f.: x*(2000*x^3 - 1110*x^2 + 1) / ((1-x)*(10*x-1)*(100*x-1)). (End) EXAMPLE ---------------------------- n ............ a(n) ---------------------------- 1 ............. 1 2 ............ 111 3 ........... 10101 4 .......... 1001001 5 ......... 100010001 6 ........ 10000100001 7 ....... 1000001000001 8 ...... 100000010000001 9 ..... 10000000100000001 10 ... 1000000001000000001 MATHEMATICA Join[{1}, LinearRecurrence[{111, -1110, 1000}, {111, 10101, 1001001}, 25]] (* G. C. Greubel, Oct 19 2016 *) PROG (PARI) Vec(-x*(2000*x^3-1110*x^2+1)/((x-1)*(10*x-1)*(100*x-1))  + O(x^100)) \\ Colin Barker, Sep 16 2013 CROSSREFS Cf. A001576, A135576, A138118, A138119, A138120, A138147, A138826. Sequence in context: A118109 A265280 A267275 * A153498 A118110 A267608 Adjacent sequences:  A135574 A135575 A135576 * A135578 A135579 A135580 KEYWORD nonn,base,less,easy AUTHOR Omar E. Pol, Feb 24 2008 STATUS approved

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Last modified November 20 10:41 EST 2017. Contains 294963 sequences.