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A152577
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a(n) = 10^(2*n - 1) + 1.
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2
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11, 1001, 100001, 10000001, 1000000001, 100000000001, 10000000000001, 1000000000000001, 100000000000000001, 10000000000000000001, 1000000000000000000001, 100000000000000000000001
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OFFSET
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1,1
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COMMENTS
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These numbers are all divisible by 11. This follows from the identity a^n - b^n = (a+b)*(a^(n-1) - a^(n-2)*b + ... + b^(n-1)) for odd values of n. In this example a=10 and b=1 so a+b = 11. The sum of digits rule for divisibility by 11 also applies.
Bisection of A000533. Also, bisection of A062397. a(n) is also A084508(n+1) written in base 2. a(n) is also A087289(n-1) written in base 2. a(n) is also the concatenation of "1", 2(n-1) digits "0" and "1". - Omar E. Pol, Dec 13 2008
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LINKS
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FORMULA
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G.f.: -11*x*(-1+10*x) / ( (100*x-1)*(x-1) ). - R. J. Mathar, Sep 01 2011
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EXAMPLE
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n ....... a(n)
1 ....... 11
2 ...... 1001
3 ..... 100001
4 .... 10000001
5 ... 1000000001
(End)
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MATHEMATICA
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LinearRecurrence[{101, -100}, {11, 1001}, 20] (* Harvey P. Dale, Nov 05 2015 *)
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PROG
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(PARI) g(n)=forstep(x=1, n, 2, y=(10^x+1); print1(y", "))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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